From a testing perspective, hard resets during test can be a BIOS, Chipset, Processor or Driver issue. First things first, check the Event Log under Administrative tools in the Control Panel. Under the System event log, just before you see the "event log service started" after your last reboot, look for any yellow warnings or red errors. If you find anything, this is where you want to start debugging.

If the system just 'restarted' and the event log did not capture a failure, then you're looking at a hardware problem. Grab a can of compressed air, take the PC outside, open the case and blow out all the dust/cobwebs. Then, making sure you're grounded, pull the memory dimms out and use the eraser on a #2 pencils to clean the copper/gold contacts. Reseat the memory in the original positions.

If it still reboots randomly, you can try updating your BIOS. this is mobo specific, so g'luck. After that, I can only suggest a format/re-install of the OS and update all your drivers.

If it's still failing, you may want to take it to a local repair center and have them run an overnight hardware diagnostic on it. g'luck either way!