How does my Desk Top Power Supply Unit ,work? (the PSU , et cetera)
Answer : Not all by itself, for sure!   related (see gaming hints)
Related to power is the CMOS NVRAM , RTC and COIN Cell.
Have no tools? see this.
For those that think a glowing LED means something, stop, and re-think that, any LED will glow at 2vdc (even less !) and means NOTHING, it only means the wall power is not 100% dead, and nothing more!
The only sure fire tool that works, is a voltmeter (DMM) or scope, (and load bank resistors for the pro)
Did you know PSU Supplies have many failure modes, not just dead.?
(fan bad or stalled in lint,  overvoltage detected, over current or under voltage detected) or just makes too much noise , so you remove it and trash it. Again most PC fail for overheating.
A bad PSU if it fails in the worst way can blow up $1000 worth of expensive electronics, so buy a good PSU, and prevent it, get one with larger fan ,quieter.

The PSU follows ATX rules.(and color coded wires)
The PC Case has a power switch, this does not actually pass 120vac (or 240v) to the power supply, at all, ever. It is 100% digital switch (amomentary closure SPST switch)
Shutdown rules: All PC made can self shut down, for many reaons, this page here is PSUs only on Desktops, but even Laptops can self shut down for most of the same reasons.
All PC DT have a processor, and if over heated it shuts its SELF down.
My fancy GFX Geforce GLU card can shut it self down (overheating tops that list) 
My Desktop can shut down for (Too low FAN RPM x3, one of 3 overheat sensors.) My fancy PSU can shut down up to 8 different ways, 5-6 are voltages/current wrong or overheated or the PSU fan stalled)
The TURN ON even happens first:
The power switch, on the case only sends a logic request for power to the MOBO input jacks (motherboard slang) Only.
The MOBO has complex logic on this pin, (and timing) The MOBO has  software (on/off ) switch on board, that is how the START button in WINDOWS can  function correctly (for shutdown) "called soft power off switch"
The MOBO can also (many) shut down the PC for other reasons, included , FANs going dead, (mine does) and OVERHEATING of key components, (the mobo maker decides this, or is programmable in BIOS as mine is)
My PC has up to 4 fans, if any of the 4 fans and the one inside the PSU goes dead, the MOBO shuts down the system so it does not get damaged, (smart no?,  and all part of the ATX system designs)
So the MOBO sees you push that Power_ON  on momentary switch on the CASE and...
The Mobo, then sends 0vdc to the power on pin 14 (old) seen below, on the PSU. The PSU quickly turns on. (pin 16 on all new PSU)
The PSU then looks at  many things,  Overvoltage , over current, and dead supplies, (newer PSU have up to 10 supply lines ! , not just the simple 5 seen in my example) If any line goes BAD, 12,5, 3.3v (+ or -) the PSU  sets power ok false.
The PSU may also look for PSU overheating and shut down. (top brands)
The MOBO watches that PowerOK pin 6. (pin 6 is and output only, tells the MOBO power IS ok do not shut me off) But the BIOS makes the rules here, the BIOS can shut down the PSU, for other reasons.)
This pin 6, tells the BIOS there is no gross PSU failure now. (here).  My PC can shut down for fan RPM too low or other overheat sensors.

This next pin must be good or all things die.  Pin 9 SB or Stand by power. (This pin on my PC even charges my cell phone with power on the PC off ,via USB jacks)
The standby power +5vsb "standby-power"
With AC power to the rear jack, this pin always has power, and the MOBO uses this power to monitor the power switch to turn on, with line cord connected. F1 fuse not blown and IC3 below doing its job 24/7.
My PSU has a 0/1 rear power switch , in the 0 position,  standby is dead, now.  (We use this if there is lightening coming soon ) (or  vacation switch)
If +5vsb goes dead, the MOBO will be dead. We use a voltmeter on pin 9 and see 5vdc there. good. if not , the mobo can not turn on the PSU.
If the PC ran for 1 second, then that means the PSU is sending POWER FAILURE warnings to the MOBO.
There is more see that here.
When Power_OK (pwr_ok or Power good) pin  is low that means FAILed;  (near 5vdc is GOOD)

Again, the MOBO can shut off,  the PSU ,  for many other reasons. (the MOBO makers book on it tells you all these facts, it be good to read this first) (mine  has over 8  rules for self shut down)

Checks Simple. (I'm a tech and have a PSU test cable jumper at all times) in logical order below easy to harder.
  1. Get rid of the dirt and lent as seen here first. (if fans stall its a very bad thing)
  2. If PSU internal fan is dead, as you push the  case PWR switch, (means no 12vdc exists.) make sure line cord is connected and wall power is good, (use a test lamp at wall jack?) and that the PSU rocker switch is set to "1" on.
  3. Make sure the power switch is wired to the mobo per the documents shown at HP.Com.  The MOBO wires to the PSU with the huge connector below, and must be fully seated. (all newer PCs have 24 pins here)
  4. Ok fan inside PSU case spins, nicely , and so do the PC chassis fans too, if fitted, (all good PCs have more fans) The CPU has a fan for sure and must spin, and on mine a GPU fan and  rear case huge fan (slow).
  5. Ok, we can do more tests, we can in fact use a magical tool called  a VOLTMETER , sold at Walmart for $20 whole bucks,  and when set to 20vdc range can measure all power pins as you push the power button.
  6. Keep in mind the 1 second rule.  You must watch power during the 1second rule. (ATX spec, rules are just that, not suggestions) I connect my meter black lead to ground then to 12vdc pin 10
  7. I power on and pin 10 is 12vdc (near) then move to all other pins, shown on the side of your PSU. (seen below in a photo of side sticker)
  8. If all power lines show good?, and the PSU sets the Powergood pin 8 to false @0v, the PSU is bad.  (yes, in the world of electronics , any of the 3,000,000 transistors (and friends) can fail.  (a hard cold fact of life)
  9. A bench test is easy, jumper pin  14 to 15(old) 16>17 (new)  and then plug in the supply to the wall power line cord. (if PSU has a rocker switch there, turn it on to "1" on.
  10. If bench tests pass,  then the MOBO has shorts some where (strip it down to find those) or the BIOS is shutting down the PSU for fans dead or overheating. (My ASUS mobo can do lots of shutdowns as seen on the BIOS page for this)
  11. A voltmeter can now read all supplies, one line at a time,  3.3v, 5v, +5vsb,  (the newer PSU's have more connectors and pins for power , to GPU video cards and more.  they need to be tested too.)The ATX spec shows colors of wires.
  12. The last check only pro tech.'s can do is use  Scope on the pins and be sure 120hz ripple is in low and not above spec. and at 20khz, if that is the noise hash you see on the lines out. (chopper noise too has  max spec)
  13. One comon way to get in trouble, is having a gutless 300watt factory PSU then add in a power sucking GFX Geforce GPU PCI card and not the PSU goes dead. (overloaded) why do that, the GFX manual told you not to....!
5vdc must be 4.75 to 5.25vdc or the logic will not be happy.
Regulation spec, (intel)

We use a scope to check ripple.  (caused by BAD CAPS inside the PSU)

Using a scope,  120hz or 10 to 40khz chooper caused, ripple max.  ,mV = millivolts  1mV = 1/1000th volt

Photo Dwg. #1  PSU connections.   To bench test the PSU, jump pins PS_ON to any ground pin.
All modern 10 year or newer PC use this ATX2 spec. PSU, it's a standard  on the right.  24 pins.  Jump 16 to 17 is safest way to force power on.
old relic ATX                               new ATX with 24 pins, but  NON ATX,  the SSF PC uses  6pin Plug,  seen here (hacked)

THE WIKI covers all this ATX stuff , read here what pin does what?

A Random found ATX power supply. (old, but shows how it all works ! really nothing beats a schematic, no?) This PSU is simplistic,  with only basic protections.

Drawing #2:  AC input is the AC line cord.  (if you look close you see that there is standby power all the time line power is connected. 
This is a SMPS design.  Q1 and Q2 are the 20khz  Chopper Oscillator. (power on , activates the chopper) IC1 controls power.

Newer ATX supplies, have up to 10 supplies inside, (up to) (newer supplies even have complex , power modulation chips that use only the power it needs, saving power and Carbon Dioxide (green) emissions.
The point here is all pins below for power must  be tested by the technician to be sure the PSU is not detecting faults, even faults on supply lines not used,  (-5 and -12v many not be used but may be monitored)
Photo: 3   Example of better PSU for gaming systems or any with powerful GPU card (graphic processor unit) PCI cards added.

If all this is Greek?  then you  learned that Electronics is not simple, find a technician to fix it.  I'm retired, now and can help.  (but only here with words and pictures)
Now I show REAL SCHEMATICS so all can learn this, not just with words.
Softpower on/ off feature is burried deep inside the glue logic, per below, and all that fan protection stuff too. (and it's own VRM rules and monitors)
Learn too that a CPU or GPU can also shut down a PC in under 1-3 seconds flat if it overheats, (magic inside the Main chips does all that by DESIGN)
The mobo has its own power regulators too (VRM), for its one special needs for special chips.  The VRM were used , because the PSU powers lines do not provide, special needs for special chips on this MOBO)
This VRM Voltage regulator Modules,, can also fail and also see the PWR-OK false and thus a drop of POWER ON line. (you can't replace these bad VRM)

Here is a year 2000 Intel 850 schematic showing the glue chips that do that.  (oh my golly, gee,, a Floppy,PATA,RAMBUS,PS2 and RS232/ Parallel printer jacks) yes, a relic.
As you know, most makers of MOBO the schematics are top secret, but how nice of Intel to show one 16 years old so folks can learn , thanks Intel !

See the signal pin  PS_ON? that goes just to one place, the PSU cable jack , this is the MOBO telling the PSU to turn on now. (you told MOBO to turn on, via the power button on the PC case)
The PSU turns on , its fan spins fast and if power is not bad, the PSU then sends, the signal, Power-good (PWRGD_Ps) to the mobo and chip below, and the PC turns fully  on, and holds  there.
The Gluechip can turn the PSU off for many reasons, (windows shut down, overheats, dead fans many,VRM errors, and more)
Or the USER pushed the shut down icon in WINDOWS. (called Softpower Down (its just a 1 bit transistor burried deed in this chip)
The below chip will be dead (or just asleep) if the 5VSB standby power is dead, from the PSU.  This supply is active full time, A.C power good to the PSU.
The +5vsb standby power line from PSU to MOBO runs over 13 circuits, see pin 2 below for that. 5vsb is complex, it allows many chips inside the PC to do the WAKE-ON functions.  (wake on LAN, wake on USB, wake on mouse,etc)
For a newer PC?, what changes?, is the GLUE LOGIC pin # and the CHIP seen below , used today. As you can see the intel engineers even call it GLUE themselves, no surprise here.

Links: (best of best) Intel has the best PDF  page, on topic.  (not surprising to me)

Now the tool-less tech answers:
 If you have no voltmeter, to do simple tests, then all you can really do is GUE$$ and swap parts.  (or do like most, get the PC fixed by a Technician)
Symptoms, BIOS dead. Screen Dead.
  1. Clean the crap out now.
  2. All  MOBO connections good, per the HP manual. (power lines ac/dc and front power switches connected)
  3. If PSU internal fan is dead so the PSU is bad. end story, (A.C wall power good) ,If the  PowerOn pin jumped to ground, shows a dead PSU then  the PSU is  END OF LIFE, TOASTED, Kaput.
  4. If PSU is ok , then mobo is bad, (unplug all things but the CPU,  then 1 stick of ram, and see if system wakes up BIOS) (pull then HDD/SSD,DVD, ALL USB, yes, all things but power) If still dead?, MOBO is bad.
  5. If pulling things , woke-up the PSU? yes,  then the last thing pulled is SHORTED AND BAD.  (keep and open mind lots of thing can short, pull them)
  6. The CPU must have a working HeatSink, and not HS compound grease gone bad, and the fan working, The heat sink on some CPU can fall off. If the HS fins are packed in lint, how can it work? (it can't so clean it)
  7. The GPU, (called a video card) must not overheat nor its fan stall, or the GPU will shut down, making the VGA, DVI, HDMI  jacks dead, (causing a screen dead.)
If nothing else, this page shows you , it don't work like you think.  
Learn too, that any LED can glow with just 2vdc, or less  and means almost nothing glowing, but flashing, it means it has failure codes , fully documented by your exact PC)

GAMING 101:  Fast Video cards, GPU's Graphic Processors.
<<<< See it in DM , device manager?

Lets say you want to game or do some fancy engineering CAT/CAM or Computer modeling?
You bought a GTX-660 (or 650 or faster?) from Nvidia or other card makers? Now what?, most watch it crash. Why ,  answer it's the AMPS DUDE !
That card needs 12vdc at "30 amps" if you read the Nvidia installer PDF line by line?
A hard cold fact that. (and keeping that fan free of lint !!!)
This card sucks big amps, and the HDD if in your system sucks 6amps each.(That's right the HDD steals power too from the 12v rails)
Card needs 30amp of power here.  (some PC's have 1 HDD, or none (SSD) others like mine have 3 or more HDD /SSD mix.)  When I say HDD, I am talking about the motor current in it. (HUGE)
The reason power goes here is for 1 reason only the PCI-e slot  can not  handle this power level at all. Best is a 2 cable PSU, for here.
Here is the correct minimum solution that always works here. 700 to 750watts,  the price range is $50 to $80... The very powerful 12vdc here is what matters.  I've run 5 years crash free at 700w. (Mine is 28a times 2)
A Thermaltake PSU 700w or more is also a good deal.  Make sure the amps are good,  some makers of PSU lie about the watts,  read the label first. 

I see endless posts by folks saying bad things about as PC, Windows, and many things, all the while violating the book on the GPU card, they can't read or can not understand, AMPS matter.
Adding a GFX card to a PC with 250watt PSU, is just silly, It is a wasted effort and endless grief watching said PC crash endlessly, or even go DEAD.
What matters most is the 12vdc rail .  The yellow wires are all 12vdc,  UP to 4 go to a single PSU regulator inside. My PSU has run crash free for 5 year now. Not one hickup. (not just 1 PC)
  if you use a proper PSU, the GPU will NOT CRASH (99% crash free, 1% are bad games,not updated) no lint packing up GPU nor CPU fans ,nor heatsinks, clean them.

Is this your PCU?
Aways clean parts OUTSIDE using Can-O-air or 30PSI shop air.

THE CMOS BUZZ word, (NVRAM, and RTC): 
How does my NVRAM work (CMOS)

version 3.  8-1-2017