On an XP machine, even though you're beyond the minimum specs for your listed games, I'd double it..

Please be a little more specific about "Im not able to Run Unreal Tournament". Does it not open at all? Does it open and run slow? Something else?

You didn't tell us which Core2 Duo processor you have installed.. Just curious..

Have you installed all the patches for the game?

The GeForce 6600, I'm guessing it's a PCIe setup? Yes? It's a fairly decent midrange card but with the newer computer, have you made sure you updated the drivers for the card? The link below shows benchmark tests that were performed with that card and UT should be able to run assuming all the other requirements are met.

http://www.neoseeker.com/Articles/Hardware/Previews/6600bench1/3.html

Hope this helps and let us know more.

Grif