You have already done all the troubleshooting steps I would recommend. At this point, this appears to be a hardware problem. Start removing unnecessary hardware and seeing if it makes a difference. I am inclined to think it is either a motherboard, CPU, or memory problem based on the behavior and the quote that I had in my recent post. I am leaning toward CPU, but any of the three could cause the CPU to behave oddly.
What RAM do you currently have in the system? Can you do the steps Dave suggested in the quote?
If you remove any components, read Avoid Static Damage to Your PC | PCWorld