I have been building my own computers since 1992. My most recent rig has been problematic and I need help; never had hardware issues like this.
Asus ROG Rampage II Extreme, Core i7-930 CPU, no tweaks or overclock, 12 Gb of Corsair RAM, DDR3-1600 matched brand, speed, timing, and latency, Radeon 5750 vid card, Corsair 950 watt p/ps, Corsair liquid cooling for CPU, 5 sata HD's, no RAID config.
About a year ago, the computer started to randomly beep thru the speakers when a key was depressed. Still does it. No problems found, configuration of Win 7 settings OK.
About 3 months ago, started randomly shutting down completely, waiting one second, and then restarting on its own. No errors can be found. Changed p/s, no fix. In last two weeks, getting worse. Win 7 tries to repair itself because it cannot restart, sometimes w/n restart. Temps and connections OK. Had message briefly during boot one time last week that CPU fan was disconnected, but CPU fan was running, pump running, and CPU is only warm to the touch. 6 fans in unit. I also hear various HDD's spooling down at time
I had similar problems with my X58 build a while back - any time I tried to run anything that didn't use the computer on idle, it would shut down. After diagnostic checks, I found it was more of a power supply issue than anything else.
Judging from that it sounds like your PSU is dying, if you have any means of testing your power connectors, that's what I would advise doing.