Case fans didn't help me. I got a 6000 RPM uber-CPU-fan. Still, I'm running faster than I should be, so I suspect a short in the processor. Yes, that can happen.

I'll bet if you replaced your processor, that would fix your entire problem.

Anyhow, the problems you're experiencing are almost exactly what I had. My computer restarted (very rarely) by itself. It got worse over time. I had a hard time booting up sometimes. Eventually, it wouldn't make it to Windows when booting. It would just shut itself off during the boot process.

I tried different cables. I tried a different video card. I tried swapping ram. I bought a new power supply. I bought a new mobo. Finally, a big motherfucking CPU fan fixed the problem. I kept all the gear though. It was all a nice upgrade over what I had.

What is it they say about silence being golden?