Wedge
Suffered from similar myself recently. Followed the advice offered previously, but simply ended up going round in circles. Removed all my additional items (extra USB cards etc) and went down to a single HDD, which I wiped completely to remove all possibility of viral infection (there weren't any).
I ran a little program that came with my motherboard and it reported that the CPU (an AMD 2000+) was running too hot (63 degrees +).
I doubted this was the cause in itself, but it all looked a little mucky in there and I decided to remove the CPU and clean all the crud off the heatsink and fan. Whilst it was off, I also bent the heat sensor that sits under the CPU slightly away from the core of the chip. Re-assembling the whole thing, I was careful to re-install the CPU and heatsink with the proper conductive paste and I also took the time to clean out the fan of the PSU. Essentially I was trying to reduce the temperature of the CPU and also reduce the 'reported' temperature of same.
Switching the machine on again, I found that the BIOS was reporting the temperature of the CPU down at 43 degrees!!!
My machine now appears to be stable, and I have had no further problems at all. In some ways this is a shame as Mrs Hat had suggested that we get a new PC!
I suspect that either my CPU was getting too hot, failing and causing the machine to shut down, or the system was detecting that the CPU appeared to be overheating, and therefore shutting down to protect it.
Good Luck!
Regards
STH