quick summary: any piece of hardware could be damaged, so replace them all. /jk
Seriously, you can test the memory using memtest86, which might safe you cash if it's okay.
You can check the temperatur of your videocard simply by touching it. If the backside (to the rear of the main GPU (=chip) is too hot to keep your finger on it, it's probably too hot; if not, it's not.
You can check the harddisk by going to the manufacturers' website, and downloading one of their test programs. If that says it's okay, it probably is.
Doing all of those things might exclude some parts. You can also remove all the non-essential bits (extra harddisks/cdroms/sound cards, etc), and slowly build your way up (playing games until it crashes), you *may* be able to get to the broken part.