Vista - Computer locks up randomly, need some help!

Hello,

I'm new to this forum and I came here because I am in need of some dire help.
I built a new computer about 1 month ago, my first build, it seemed to work perfectly and I was very pleased, but recently I have been getting random lockups. It occured during games, during web browsing, even on bootup. However, sometimes it works fine for hours doing games or just watching movies. When it does lockup, I have to reset so no error report shows, however, when it locked up on bootup, it BSOD and restarted automatically and an error report was shown in Windows, I don't have it right now since I am on my laptop but if required, I will retrive it.
I performed scan disk and scanned my computer using Sophos Antivirus. It detected some spyware/virus, which I don't know how it got there, the only things I installed were games and some legit programs. One of the detected spyware/virus, not sure what it is exactly, is Generic-A I believe, which I read poses a high risk. I cleaned it up along with 2 others and for a few days it seemed to work fine but just today it locked up. Is it a hardware problem, overheating? I have 4 fans, 2 on side, 1 in front and 1 in back. System temp under 50C I beleive, CPU get as high as 57C. Perhaps the spyware/virus did not get removed? I don't know what to do now, perhaps reseat memory and CPU?

System specs:
AMD X2 64 6000+
ASRock 780GXE
Sapphire HD4870 512mb
2x2GB OCZ Reaper PC2 6400
610w PcPower and Cooling
250gb SATA Seagate
160gb IDE Seagate
Vista Ultimate 32bit

One thing I should add, I initially started off with a 250gb SATA hard drive that I bought new, but I wanted the files on my old Dell computer, so I put in the 160gb IDE hard drive. Perhaps this contributed to the lockups? I am able to play games that were on the old hard drive in this new computer like Call of Duty 4.

I'm getting kind of frustrated with this problem and very worried, I put quite a bit of money(for me anyways) on this computer and hate to see it like this.

Any suggestions would be appreciated.