Some P4's run hot yet, but I believe the D9xx series are a bit cooler, esp, with good cooling. I don't know what cooling you have. I assume the program you use to put a load on the cores does test the CPU thoroughly. I would try prime95, just for the heck of it... see if any core fails.
Other than that, the thing that comes to mind is drivers. You seem to have tried several cards and onboard now. I am not sure which driver you used initially, but maybe that install did not go right, and the problems that arose with that never were fully fixed when using subsequent drivers.
I'd try to completely clean out the drivers, using drivercleaner pro. Remove any and all drivers from the cards you used (either ATI or nVidia) and go from there.
Another possibility is some sort of odd conflict with components... maybe a PCI card or so that tries to access the same IRQ or memory address as your video does?
OTherwise, I am not sure...