PC powers off at random times

I had a motherboard that did that. The cause was I accidentally installed a 1394 cable into a USB spot and it permanently damaged the motherboard by putting voltage where voltage doesn't belong. It exhibited the exact same symptoms. I lucked out because it reset seldom enough that my computer was still mostly usable. It's a common error, and if your computer has been acting up since you built it, this is a likely cause.

Unfortunately, no amount of tinkering will be able to fix it, you might be able to permanently workaround the issue by completely disabling USB/1394 in BIOS though.

No way to know if this is what's causing your issue though, unless you can recall accidentally doing the same thing during build.

I believe that I've found the answer. Notsosure's link to the Toshiba thread really helped in figuring out the logic behind this mess.

What's happening is that certain capacitors on the motherboard that regulate the current of the CPU have started to fail. So whenever the CPU changes its clock speed or multiplier, the capacitors do not deliver the required voltage to it and the CPU malfunctions. This causes the system to reboot. Some users have fixed the issue by replacing the faulty capacitors (they are located directly behind the CPU socket on the motherboard).

Intel refers to this throttling technology as Speedstep. Windows Safe Mode seems to not use this CPU function which is why the system doesn't reboot in that mode. Disabling all the processors in Device Manager prevents normal Windows mode from using it as well. As long as the CPU doesn't use Speedstep, no spontaneous reboots will occur.