Vista - Computer locks up randomly

Hello,

My new computer locks up randomly. Sometimes I can play games for hours without locking up, other times it locks up within 10 minutes of bootup, once even during bootup after which it gave a BSOD. I don't think it's a heat problem, perhaps my memory or hard drives? Performed scan disk, virus scan, had a few spyware which I cleaned up. Have not performed memtest, do you think I should?

Specs:
AMD X2 64 6000+
ASRock 780GXE
OCZ Reaper 2x2gb PC2 6400
Sapphire HD 4870 512mb
Seagate Barracuda 250gb SATA
Western Digital 160gb IDE
PcPower & Cooling 610watt Silencer

Any suggestions?

SInce Memtest is included in Vista as an option running it to see if any faults are detected wouldn't hurt any. If 0% are indicated then you would simply move on to the next item and take notes on any information displayed on the BSOD as well as reviewing the information in event viewer logs. The problem often turns out to be software or device driver related.