memtest works well, but I've had an issue where ram was failing and memtest didn't pick it up. I generally just do 1 pass as that'll pick up most problems. More than 1 pass might be needed if you're overclocking the ram to really see if anything is wrong. Though nowadays I just don't overclock the ram since the performance difference is very small.
I won't rule out that your computer is unstable, but I'm betting on it being more of a background program or driver issue. Normally when others have the same issue with the game, it tends to be some little setting or something with certain drivers/programs. The game itself might be buggy, but obviously is playable on Win7 64bit.
I must ask, why are you not running an antivirus? At the very least I would grab a free one. I personally use the free edition of avira, which is highly rated. Then go into settings and turn off all the notifications. You'll still get a few popups here n there, but you'll get used to just clicking it as soon as it pops up. AVG doesn't have those popups, but I have read of a few games having problems with AVG. Normally I'll install AVG for friends/family who don't game and avira for those who do.