From your description, sounds like the CPU fan is dying.
You went through all the usual stuff, and it appers nothing worked -- but I have to ask -- does your motherboard have a BIOS jumper? If so, then switch the jumper to the other two pins next time you reset the BIOS. That should work.
I had similar problems with an older HP Media Center PC -- in that it stopped recognizing the keyboard after a while.
What worked for me was switching out the expensive HP keyboard with a cheap $10 USB keyboard. I did that, reset the CMOS (using the jumper and removing the battery), rebooted (with the cheap keyboard connected) and it worked fine after that -- until my client decided to go back to using the HP keyboard, and then we had to reset it again.
Also, I would look into replacing the CPU fan -- as that's a lot cheaper than replacing the CPU.
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