This situation is a bit... Complicated. It involves a power surge.

I had an old PC and a power surge virtually ruined everything in my computer except for my dvd-rom drive and, to the best of my knowledge, my processor. Allow me to elaborate:

A power surge caused my power supply to make this high pitched sound. Not thinking much of it and being ignorant to the sound resulted in a small shock one day which rendered what appeared to be at first, my motherboard and my power supply useless. When everything was plugged in properly, my computer failed to turn on. When the power was cut from the hard drive, the computer failed to show any signs of functionality (ram, video card, mother board, with the exception of the fans working). Since the computer never made it to post-bios in this state, it was decided to buy a new power supply and a motherboard (The models of which I will give later)

I started by replacing my power supply with one of an equivalent wattage (500W) and my mother board. Upon plugging everything successfully (RAM was not in as my old ram was DDR and I thus required DDR3 ram) into my motherboard and hardware, the computer failed to turn on, but when I cut the power from the hard drive- the mother board gave me its standard 3 beeps to let me know that there was no ram in the computer. This led me to purchase a new hard drive and the required ram and set it all up.

Everything has been installed now with the new motherboard, hard drive, ram, and power supply along with the old processor, fan, heat sink, video card, and dvd-rom drive. At first my computer turned on like a charm. I thought everything was fine and it was just a matter of installing windows- but for no apparent reason- the computer turned off (first beep was made and computer made it to the post bios [correct terminology?]). What appears to happen, is the computer functions normally but eventually just shuts off. The only thing that logically remains is the processor. I don't think the processor is overheating because the fan is the exact same one from the old motherboard. I considered the potential for my computer to be underpowered, but upon calling a technician and asking for help I was told that based on the video card and mother board that I'd informed him of that it was unlikely to be the case (Yet this hasn't been ruled out just yet).

A symptom that is leading me to believe that my computer is underpowered is that the fans are sluggish to turn on upon starting my computer. I press the power button and after a few seconds, they finally start to spin. It is important to note that the more frequently I turn on the computer, the less time it's capable of remaining on- which leads to an overheating issue. I'm genuinely lost. Does anyone know the answer?

Motherboard: P5P43TD is the model number
Processor: 3.0Ghz Intel (Other specifications not available)
Ram: DDR3 2x2GB (model number not really relevant, I don't think)
Power Supply: 500W (again, model number not really relevant I don't think)
Video Card: NVidia 7900GT
HDD: 1TB 64 MB Cache 7200 rpm --- Not relevant, as even without this plugged in, the computer still turned off after a period of time.

"I don't think the processor is overheating because the fan is" The one thing that I suspect that you DID'T replace is the CPU. CPU's will light up/turn on but will do nothing. Basically, the lights are on but no one's home. Whatever it was that zapped the rest of the hardware got the CPU as well. Whatever the damage the fan(s) is a non-relevant matter. You might also consider a computer grade power strip with some spike/surge protection.