Yes, hardware problems can cause DEP errors, although they are more likely caused by a virus. But from everything you said, I'd bet that there's something wrong with the hardware, whether it's overheating or something's failing is hard to say. But if the problem started randomly, heat might not be the problem.
Just to be on the safe side, before ruling out a virus, I agree that you should find a liveCD distro with clamscan and do a sweep for viruses. If nothing is found, which I suspect will be the case, start looking at possible hardware problems, including overheating.