You would see a cacophony of errors, symptoms and a collection of BSOD numbers. You didn't list your PSU make/model/details but I'd like to see 550 or higher Watts in a good size case with a +12V Single rail.
You can test power supplies using a Volt meter and the Green Wire test in a pinch or a PSU tester or the more common method of adding 100 or more Watts (and moving to single rail if this is not) to your NEW PSU.
OS: Microsoft Windows 7
Graphics Card: Nvidia GeForce GTX 560 Ti
Processor: Intel Corte i7-2600K CPU @ 3.40GHz (8 CPUS)
So, I was playing skyrim and the computer restarted out of the blue (at first I though this was a power surge). I played again and about half an hour in, ir restarted again. I checked and the computer was a tad hot, so I decided to stop playing and even placed a fan directly at the case. I decided to stream a documentary and even set up a task for the computer to turn itself off after 2 hours. (I imagined I would fall asleep) After about 10 minutes, the computer restarted itself again. So I started trouble shooting. I closed nvidia panel, turned off the automatic restart function on my pc, opened the case and checked that every cable and card was well connected to the motherboard/power source. And about 5 restarts later (each one lasting in between 5 to 10 minutes) The computer just wouldn't start again. It shows no sign of power at all so I'm thinking it could be the power source, but It doesn't seem to explain all of the symptoms to me. Or could it be that on top of whatever's causing the computer to restart over and over again the power source also got damaged?