With that much money, you can get something really nice
Basically, you want to be looking for a Core 2 Duo processor (or CPU) - these are the latest and wipe the floor with every else, and they are not even very expensive
For a gaming PC, the next most important part is the graphics card - looking for either a X1800XT, a X1900XT (or XTX) or a 7900GT or GTX. The 7950GX2's are just a waste of money, they overheat causing corruption and due to dodgy drivers an upgrade is not wise (that is my opinion based on everything I've read).
I would definitely recommend Voodoo PCs, who do excellent PCs. Unfourtunately, their cheapest PC is $3200, which is out your budget, and even then a lot of that money is for the custom paint job.
I know you said not to go over budget, but I was blown out of the water by this one:
Core 2 Duo X6800 (the best processor in the world)
1GB RAM (enough
, and your son or your local internet cafe could always upgrade later for about $100)
2 x ATi Radeon X1900XTXs in Crossfire - pretty much the most powerful combo of graphics cards possible
Watercooling - quieter than air cooling, but more expensive
Camoflage spray-painted case
If he has the screen I'm guessing he has the other essentials - speakers, keyboard, mouse. If not, maybe he could pay half which would keep your costs down?
Seriously, that is an amazing PC!