Hey, just want to give my 2 cents. My parent's computer that I built for them 5 months ago recently also started having this issue. Random restarts. Occurs completely randomly throughout the day and on any application. e.g. Surfing web, typing in excel or just idling. No blue screen, error messages or anything. Just a sudden power off and automatic power on.
Wah this problem was so hard to resolve. I know that generally its either A) PSU or B) Motherboard. I tried resetting bios, scanning for malware, running a hdd check and doing a memtest for ram to eliminate possible candidates. My worst fear was that it would be motherboard failure. Very ma fan.
In the end, I took a spare power supply to replace it. And everything is working fine now. I replaced the seasonic S12G 450w powersupply with a 5 year old OCZ ModXStream 620w powersupply and the random restarts have stopped thus far. It has been about a week already, still smooth sailing.
My recommendation would be go through the standard checks to eliminate culprits and then try to get someone to lend you a working power supply to check. If not, then I think its motherboard lo.