If it occurs after the drive is removed its almost for sure a hardware problem. It COULD be a bios virus but that would be like me telling you I've discovered a cave with living woolly mammoths. They haven't been seen in the wild in years and their attack vectors are mostly dried up.
From what it sounds like the board itself is unstable. The other places to look are the power delivery system (which is a board replace as well) and if it isn't heating up and it turns on in the first place.
Personally I think it might just be its time. Its an older Turion X2, you've owned it a good 2-3 years at the very least. Those Nvidia chipsets in those machines was notorious for having the solder melt and the northbridge fall into the board and move off of the thing. Thats not really what this sounds like, but who knows what else could be wrong with those boards.