I know that one symptom of a bad RAM DIMM is that the screen will quickly go black and cut out, then cut back in again at random intervals. You might also want to check youcase temp, in some / most modern PC's the BIOS had a temp cut off ... you can set it from around 55 - 65 C if your temp goes above its set limit, your pc will reboot, i think its based mostly on CPU temperature, so you might have some kind of fault with your CPU fan maybe, or the fitting of the fan on teh CPU might have been disturbed in some way, either will cause the CPU temp to rise, thus your PC rebooting.
I do think however its more likely that its a hardware thing not so much a software or virii thing. To check your CPU temp try this.
Power on your pc, you should see something saying "Press *** to enter setup" where *** = either 'DEL', 'F1' or something simalar, also might say "to enter 'BIOS'"
once in bios just look through your options, maybe 'advanced features' or something along them line, and look for Power management or simalar.
once you found that, you should see something that will tell you the CPU temp and you can set your own limits or turn off, however turning off the limitations ( if it is the fan ) could possibly damage / blow your CPU. just look at the temp, see if its aobve 65 / 70, if so, its time to open the case and check out the fan, and how its sitting on the CPU.
Good luck