How to go about computer problem solving

A friend of mine (a mail carrier) had a computer given to him by a customer (Doctor). As my friend (John) put it, this customer has more money then patience (not patients :-D ). The Doctor had been having problems with it and just gave it to John and bought another one. John has very little experience with computers and so I told hime to bring it over and I'd take a look at it.

Here's the stats on it:
Gateway GT5644E desktop computer
Athlon 64 X2 5000+ cpu (2.6GHz)
Windows Vista
2000 MHz system bus
Chipset Nvidia Geforce 6150SE
3 gig DDR2 memory (677 MHz)
Hard Drive 400 GB SATA
DVD
Media Card Reader 15-in-1 high speed digital media manager
Geforce 8300GS

Instead of coming with disks it uses HD partition to hold the software/os, so I reinstalled the OS (and all the extra crap that gateway puts on the computer that John doesn't need).
Then I loaded CODWAW on it and tried it out with no problems. Even thougbh it would still freeze on boot up at times. Last night when he tried to get online and play the computer would freeze.

I used memtest and that worked with no problems. But now, whats the best way to proceed to find the problem. Are there any programs that can help?

 

Hmm, remove all peripherals and try to boot again, plus all interior boards besides the video card, reboot and see which one shafts you as you reinstall them..