Honestly, it Does sound more like a PC hardware problem than a Windows problem.
Even something as simple as a loose power cord. (I've actually taken a service call on that same thing)
Or loose connectors inside the PC. Very common on a Desktop PC and less common on a Laptop PC.
I'd go through the entire system and make sure that every electrical connector is properly seated, especially at the mother board level. Replace the CMOS battery if it's less than three years old, while you're at it. Never hurts to have a fresh CMOS battery in your PC.
And, like was mentioned in a previous post.....a dirty CPU cooler can cause overheating which can cause a shutdown and reboot situation.
Also, a failing cooling fan in the PSU can cause the same condition. I've replaced dozens of those.
A clean machine is usually a happy machine!
Good Luck!
TM
PS: I was actually given a beautiful HP Laptop with the BIG screen, because it would boot up and immediately crash. I found that the CPU cooling fan was frozen (stuck) solid. Looking in through the air intake holes in the base plate, I could see the fan was not turning, and when I tried to turn it manually, I could NOT. I really didn't want to tear the laptop all apart to get to that little fan, and take the chance that I could buy a replacement, so I did the next best thing.
I cut out the plastic grill over that fan, and Glued a 2", 12v fan over the hole to blow room air into the Laptop, thus cooling the CPU, etc.
I connected an external 12v power supply to the fan and then set the laptop up on Printer Stands, so the new fan was up off of the desktop.
It's no longer portable, but I have a great little AIO PC, sitting there happily running Windows 8.1/Pro/64. I'm currently using an external Keyboard and mouse with my new AIO PC. It makes me a great Backup PC. Waste not, want not!