Do any of the system fans or CPU fan run?
My last PC, I was in the middle of playing BF2, I was flying a Helicopter,
all of a sudden my PC froze. The sound became a very HIGH pitch annoying sound. After trying a hard boot, my system wouldn't past post. I was also getting BIOS beeps.
I spent a few minutes doing what I suggested above and found out that the 1st dimm channel wasn't working. the second worked fine. And all the ram worked fine in the 2nd channel. But as soon as I put the ram in the first.... no POST.
I mean, this may not be the issue. But, i would start there. May-be your CPU is overheating and throttling. May-be your memory has errors. May-be your videocard is shot...