Panic !
My PC boots or not, but  my data is gone!  What can I do? , answer , plenty!   
My PC is dead,  and seems I can  not backup my data? (sure your  can ! if the HDD/SDD is not brick dead.)

There are only 2 ways to back up, 1: external media (or servers you own) or 2:  the Cloud (fools trust cloud, IMO)
If all you do is play MS. Solitaire, just do a fresh OS install and end this worry.

The older the OS (Operating  System) the more likely this will happen , if running MS XP it's mostly hopeless now, as its not supported now for 3 years, and is a virus magnet.
News flash: (4/2017 update: Vista is now officially dead too)

There are 2 kinds of users, (really lots more but..) 1: backs up every day , or 2: never !  ( a wise Student or Business professional has 2 backups every day)  One, say on a server and one on a USB memory stick.
Backup as often,as you can afford to lose data, for gamers it's not too important unless game progress is Okay to loose.
end backup rants...
Example below is of a HP Laptop, Mfg. date: circa 2010 ,

The PC can fail in 100's of ways. (any PC, no matter is shape,size or weight class , from note pad to desktop to a server.)
I will now show how to recover data (if even possible) in the most worst cases,  (less to harder cases)
If the HDD is dead silent, motor dead, and power to it 12vdc and 5vdc or good, then the HDD is gone (DEAD) as is your data gone (sure the rich can get it back some of it or all , for $1000's of bucks.)
The best way to get data off any disks is move it to a working PC and retrieve it.
The other best way is use a boot media (CD/Usb stick) with live Linux running, or Windows LIVE PE boot media (DVD/Stick) with live W7/W8/W10, (I have them all , so I can get anyones data fast and sure)

Hint 1: if running windows 7 to 10 and lost your CLOUD password go there and fix it.
Any other lost PW or dead OS or dead HDD, it is now time to backup that data you can not reach easy.

Way 1:
The Virus  killed your only log-in to say Windows 7,8,10.  (there is never limits on what bad a Virus can do... not really) AS CAN A BAD Hard DISK (HDD)! (we are recovering a Local account here)
The savvy owner has a 2nd or 3rd account on the PC as Administrator, or Windows will not let you access other accounts. (  Say from Admin to Say Larry's account) (the guest account is useless here)
Bam   on, this PC, it  has no Admin account or is corrupted or the owner has only  guest account and the default offline admin was never activated.  (as is usually the case)
The owner now wants to backup his/her data (I will now use the word his/him to mean his/her from now on , dig?)

My HP has the MAGIC  F11 key that takes me to the "HP Recovery manager",  I click backup and the manager tells me I can backup, but if this works you are home free to , fresh Install HP Windows, with F11 the 2nd time.
HP offers 2 choices, Backup or Fresh Install (kills all data). (unlike Windows OEM K choice, install and kill data)  (a 3rd choice is buy a Windows Retail disk W10 and do an upgrade now, (keeps data/apps)
Way 2:
The owner (or tech)  now boots to Windows Live PE 10,  (off stick CD/DVD are now dead meat)  {built using Rufus app} The Stick boots,  on my HP gear hit F9 (HP forced boot mode ,love it)
I boot to PE,  and my disk is chock full of apps.
I then try to access my data, found in C:\users\username\   {  replace username with your account name seen there, that you want to retrieve} (my documents, tops the list , in there)
Warning windows is now mutated to extreme, security now (w7 is even patched (updates) to be more like w10 now) So do not be surprised that any Windows PE disk , will block you from files that are yours.
One time I tried  (2017) the PE told me , to give owners PW, and I did that, but the Virus had killed the PW code some how.  (dead log in) Yup, worst case can be dicey....
If you have and Admin (true) login on that system,  you can get all files if not corrupted. (directly and the most easy) Always have  Admin account, activate the hidden one.(use it only for emergencies like this)
Lets say this fails.  What then.?
Way2: may fail (permissions blocks), so you remove your offending HDD and connect it to anyother PC as drive 2,  and get your data. from your Users account above. (if it lets you)
Best way now (2017) is to avoid windows totally. (the above ways, do  work on older OS !)

Way3: (in all cases here , the HDD spins ok, and some data is there)
Next is Linux.  (you have no other choice now, Windows failed you "my point of view")
Linux cares not beans about Windows strict file security rules, to Linux it's just data files, so long as no partition corruption or NTFS structures are damaged, I will cover that last (that is worst,worst case)

I take my Rufus APP v2.13. Portable version , I like, and build a USB stick from ISO,  best ISO is the HUGE one 4Gb, called the full DVD version.V7.6 EN is what I have. (or newer, newer is always better in Linux world)
 (the 5 USA links are dead, so here is England Servers, but get the ones ending in EN.ISO for English not DE for German )

Rufus is easy to use, Google how to use it. (one can also burn a DVD with free imgburn.exe (google it), get them from the real makers site, never use download-virus-site-dot-com.
Linux is not too scary now, with Windows drive automounts, etc.  Desktop and file explores, (many).  IMO
The newest Linux is best, so it can operate newer PC chips , wifi , wired and mount USB drives instantly.   Here  I am doing this step.,..
 1,2,3 steps is all it is. (my stick is in D: make sure you get this correct. "look, then leap" )
If your PC can boot a stick this works for sure. (if not, use a DVD disk linux live boot.)

We now boot that stick and retriever all my USER/username ,data and put said data on any external media. (external means not your failing HDD)  SEE EXAMPLE HERE.

Last, is what we call computer forensics today,  (old name, data recovery)  (forensics goes way deeper...and can be overkill, but is a choice)
There are some real great and expensive software, sold to get data from corrupted places or deleted files. (Google finds them and let your pocket book tell you what to do? I can't) {and endless changing topic if ever there was}

Here are some free choices, read how to use them by clicking the links.
The first one can repair corrupted structures.
The next one,  can give you access to all data,where possible. (some software can find the , impossible, but not if the sectors were over written say after you deleted a file)
I'm using open links here, so you  can see you are leaving my site.

Be aware, that  some Software (Forensic) can even recover part of a document.  (say a 300 page thesis and gets 290 pages?) Or  all of a deleted file.
Learn to use  your PC more wisely, each day you edit some huge document or work, save it each day with a name (number)  , lets say its a huge PDF,
Day1,  save as (mystory1.pdf) then day2, save it as (mystory2.pdf).
Then at the end of the week you have 7 files or in a month 28-31 files, then later if you are doing a recovery, you never loose more than one days work.
On old main frame computers this happened automatically, like a DEC, VAX
Sure, every day backup to other media, cloud or server.  (best is to backup off site, so if the PC is lost/stolen or say lightening blew it to kingdom come, you still have every days work, every single one.

Here is my wish to you,that your DATA is easy to  find, and super easy to backup.

My PCs all have 2nd SSD, (hdd) so I can backup to the second drive at any time, and to a stick my data.  (my laptop the optical drive is removed and has  SSD caddy there now)
This gives me backups in 3 places,  C:  , D: and STICK, (all 3 can never crash at once, but could be stolen,  for a cure for that, is put your data in your off site server or Cloud)

My last hint , always have an External HDD drive,(SSD) that is eSata ready so you can back up and then turn it off.
I have 3 backups. (besides my PC's C: drive)  (this adds up to 4)
Blu-ray BD-R (CD-R is ok so is DVD-R) (can be USB external drive used for backups)
External HDD (2TB or more) eStata best, USB 2nd best.
and a USB STICK (the really paranoid use rotating USB , my friend uses 7 USB sticks, marked Monday to Sunday, for the reason , why trust just 1?) once bitten 10 times shy?. (in the world of creativity)

Good LUCK !  "My the force be with you"

The early bird gets the worm, but the 2nd mouse gets the cheese. (be backed up and win)

Examples (Knoppix)  See the cheat sheet,  HERE: I use this "knoppix no3d" at boot.          (RTF HERE)
Ubuntu Linux is my favorite, but the below, works very very well. I even tested this on a Windows 10 HDD.
Knoppix running, now...
The files are all completely accessible.  I can copy any thing I want to anywhere. for sure that /users/ folder.

I also have Acronis backup here to backup anything I want.
This company Acronis , you can make a  boot disk and can backup anything, but they charge money for that.(feature)

My neighbor just called, and her account was corrupted and could not login,  she had no 2nd admin acount, so zero ways to login.
I hot patched, the SAM , it logs in now and is still corrupted. (Virus damaged, HDD is ok.)
But I backed up all her data 9GB,to my extra  external eSATA HDD drive and did the HP F11 restore.
 (she how has all her music back vast, , 17gigs of photos and Quicken data. 60 versions, with W7 fresh installed.)
I used Acronis backup CD to get her data, from User/username .

Version 2.  4-8-2017  By Deadpool.   (I owned a PC in 1978,before the name was even coined,  Ran Digital Research  CPM then) (Northstar computers)  "DOS was counterfeited CPM" IMO ( a toy by today's standard)