I want to place a bet on your PSU being under powered. If you can, run HWMonitor from CPUID.com and give us your idle, and maximum temperatures while sitting at the desktop. Also, what brand and model is your PSU? If you have a cheapy, sure, it can put out power, but once things get toasty, it will struggle to put that power out, then flat out trip an internal breaker if equipped and shut the system down.
The reason I suspect the PSU, you are having to remove power for a short period of time, to get the breaker to reset.
No offense to Ksod, but a faulty system install, won't cause this type of behavior, but a bad logic board on the hard drive can, but it is very rare, and requires the board to short out to the point the drive will no longer function.
In order to turn my computer back on I have to unplug it for about 7-8 seconds and then it will turn back on.
Also, OP, sometimes it takes us awhile to get to posts around here.