Considering that the Phenom II x4 965 BE is a little over 1.0GHz faster then the C2Q Q8200, the 965 BE should provide a little better performance. The Phenom II X4 series is about as powerful as the 2nd generation C2Q CPUs (Yorkfield) on a clock for clock basis.
Not sure if it is worth justifying the cost of buying a new motherboard and RAM in addition to the 965BE.
The dual core Core i3-2100 can easily outperform the 965 BE in games. Therefore, I would go with that or save up a little more for a Core i5 CPU for even better performance.
AMD video cards works in nVidia motherboards. nVidia video cards work in AMD motherboards.