Your computer locks up at random times eh?
If its a new build, that rules out spyware/viruses.
Go into your BIOS and monitor your voltage for a few minutes. If 12V drops below 11 votes and 5V drops below 4, the problem is your PSU.
Try setting your screen saver to never come on and your computer to never hibernate, and let it idle, see if it still freezes.
"Just because I'm sitting between you idiots doesn't mean I want to go skiing!"