You're worried about a Core 2 Duo being slow?? I agree with shery, the C2D is a big jump from a P4.
That rig looks like it can easily handle Win7-64bit.
I was able to play even old funky late 1990s games using Win7 64bit.
Need for Speed Run isn't very demanding.
I still have a Core 2 quad and able to run Crysis, Farcry2, Battlefield 3, Arma 2, Stalker, etc on max settings. (ok Arma 2 on max is a little stretch)
Again, you can wait for Win 8 which should use even less resources than Win 7 or XP. Win-7 (without Aero) and XP use about the same resources, but 7 does/has more)