Actually, the game runs on both. What i mean is, if you get a kick **** graphics card, your CPU WILL bottleneck it. If i were you, i'd spring for a new GPU for now, and then plan on upgrading everything else when you have the time/money.
Edit: the Core2 line has proven to be sub par. You really want to jump up to i7 series if you want to improve game quality. I'm running a good graphics card, but my CPU (AMD 64 X2 6000+) is bottlenecking it. And my CPU is almost as good as yours is (benchmark wise).
Edited, Sep 4th 2010 12:24am by Teneleven