Your computer is fine. Moving from a dual core to a quad core CPU won't give you the gains that you expect. Dual cores were almost better than quad cores a while ago just for gaming since not many games can utilize the full benefit of a quad core setup.
Quad core is more for doing rendering work and long compilations where the work can easily be distributed. While the latest quad cores (nihilum) may put your dual core to shame, upgrading to one of these would be significant as you would have to replace your mobo. And again, you wouldn't see the gains that you expect. The E8400 was a pretty sturdy chip if memory serves, and great for overclocking.
If I were you, I'd wait and save up. Then upgrade in about a year from now when the 6cores come out. Spend like $1500 on a full system upgrade. And then enjoy it for another 4-5 years.