Desktop Processor Overheating Problem

[AlaDes]

I have a custom built desktop PC with an Asus motherboard and an AMD 939 processor that I have not been able to track down the cause of the processor overheating. Just allowing the unit to sit idle it's not a huge issue. The minute I start using a browser or other software, which puts a load on it, the temperature starts climbing to as high as 250 degrees Fahrenheit and ultimately shuts down. I've never gotten a BSOD, or noticed the speed of the computer getting slower, just temp rising quickly, then shutdown.
This is one of my personal computers, so I haven't really spent allot of time on it, nor am I too worried about fixing it, because it's an older machine anyways. The only reason I'd like to figure it out is because I may one day face a similar issue with a client's PC.
I have taken this PC completely apart, cleaned EVERYTHING, replaced/added case fans, swapped memory modules, replaced the power supply, cleaned and reapplied thermal paste (arctic silver) to the processor numerous times, replaced the processor heat-sink and fan with a new one, and even replaced the heat-sink hold down with an identical one from another motherboard.
With replacing just about everything in this unit, except the motherboard, processor, hard drive, and case, I can not see anything else that could be bad other than the motherboard or processor. I did notice that when I replaced the heat-sink hold down it did help a little at first but then gradually started getting worse again over time.
Has anyone ever seen a processor with a surface defect that could be causing this problem? One that could cause enough of a gap between the processor and heat-sink that would cause it to overheat? Or could it actually be a bad motherboard or HDD?