My Lovely Lady's computer froze up this morning after she simply opened her AOL email (please don't laugh, one day we WILL get he on gmail).
 
I tried everything I could to get it to respond. Nothing. No start icon, no ctl-alt-delte, nada.
 
So I powered it down. Upon power up we get the DELL icon (it's an off the shelf Dell computer) and the spinning dots. At one point I let it run for nearly 30 minutes.
 
Then I decided that maybe I could boot to the bios to turn off the Dell icon (and maybe see more boot up diagnostics). I did get the F2 Help and F12 Settings prompt but F12 did not respond (maybe because it's a wireless keyboard?). None the less the computer then displayed "Preparing Automatic Recovery" after which a black screen appeared and the "Diagnosing Your PC". Ultimately I was given a choice to Restart or Advanced options. 
 
Well, Restart just got me back to the same viscipus cycle. Will not boot to Windows 8.1. So back to the Restart or Advanced options for me.
 
Went to the Advanced choice and saw a menu that I could ultimately get to choosing a Windows Restart point. The lastest one was  an automatic System Restore point on 1/20/2017. I chose that one. After 15 minutes of restoring the files (which to me is an indication that the boot drive is in some sort of working order) I'm now back the simple display of the Dell icon and the spinning dots for at least 15 minutes now?
 
WTH? Any ideas?

http://www.dell.com/support/article/us/en/19/266787/en?c=us&s=dhs&cs=19&l=en
 
If it were not a Dell, then booting from an installation disk might be an option that would let you learn more. 

Update: It finally booted to the Start screen. Mouse was very slow. Got to click on the Desktop icon. Frozen again.
 
Slart. your link says to get to the diagnostics I have to press f12 at the spalsh screen but I can't seem to get that to work with the cordless keyboard. I'll have to try with a wired keyboard. 

Update # 2: Desktop is loading very slow. I'm beginning to suspect the power supply even though the fan is spinning. The case fan is spinning also.
 

Update #3. Taking it to Geek Squad. We bought the computer from Best Buy; not that it mattes since it was purchased in July 2015. They are just conveniently located to us.
 
I'm 99% certain it's a power supply.
 

Bailed on Geek Squad. $100 up front may take 3-5 days. This is her work computer.
 
Finally got into Dell's ePsa diagnostics. Did a quick system check. No probs. Geek Squad guy felt it was a hard drive prob. Doing a full Hard Drive test. Up to 90% (over 1 hour now). We'll see. 
 

HD is my guess also.
 
If you ever get the chance, look in Events ...

Me too. 
 
 

Solved with the ordering of a Recovery Disk.
 
So far does not appear to have been a disk problem.