How does my Desk Top Power Supply Unit ,work? (the PSU ,et cetera)
Answer : Not all by itself, for sure!
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.?  Some can even make Noise and kill any PC dead as a door nail, (a hard cold fact) and worse, it can blow up a nice $300 micro processor chip.

The PSU follows ATX rules.
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 (momentary closure SPST switch)
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 or restart) this magic hidden 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 seen below, on the PSU. The PSU quickly turns on.
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 MOBO watches that Powergood line. (the rules can vary by maker of each MOBO that is  there CHOICE and CALL)
The standby power +5vsb "standby-power"(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 doing its job 24/7.
If +5vsb goes dead, the MOBO will be dead. (and owner of PC sees the power switch is DEAD as a door nail) 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) is low that means FAILed;  (near 5vdc is GOOD)
The PSU has a maximum decision time on this line of 1000mS, 1 full second, that mean the MOBO turns it on, then watches Powergood after 1second, if its low , it floats the power on pin and it goes to 5vdc an the PSU shuts off.
Again, the MOBO can shut off,  the power, to the PSU for many other reasons. (the MOBO makers book on it tells you all these facts, it be good to read this first)

Checks Simple. (I'm a tech and have a PSU test cable jumper at all times) in logical order below easy to harder.
  1. If PSU internal fan is dead as you push case 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.
  2. 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.
  3. 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).
  4. 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.
  5. 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
  6. 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)
  7. 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)
  8. A bench test is easy, jumper pin  14 to 15,  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.
  9. 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.)
  10. 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)
5vdc must be 4.75 to 5.25vdc or the logic will not be happy.
Regulation spec, (intel)

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

Photo Dwg. #1

Random found ATX power supply.
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 Chopper Oscillator.

Newer ATX supplies, have 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

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. All  MOBO connections good, per the HP manual. (power lines ac/dc and front power switches connected)
  2. If PSU internal fan is dead the PSU is bad. end story, (A.C wall power good) ,If the  pin 14 jumped to 15 shows a dead PSU then  the PSU is  END OF LIFE, TOASTED, Kaput.
  3. 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.
  4. If pulling things , woke-up the PSU? yes,  then the last thing pulled is SHORTED AND BAD.
  5. 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)
  6. The GPU, (called a video card) must not overheat, or the GPU will shut down, making the VGA, DVI, HDMI  jacks dead, (causing screen dead.)
If nothing else, this page shows you , it don't work like you think and for sure  has millions of transistors (and friends) to fail.  It is not a flashlight or a toaster.
Learn too, that and LED can glow with just 2vdc, or less  and means almost nothing glowing, but flashing, it means it has failure codes ,fully documented by

version 2.  4-1-2017