Your CPU can handle a MUCH better graphics card, but your Power Supply can't.
Unless you're playing older games, or current games on LOW quality you'll have to invest in a new graphics card AND power supply.
Personally, I'd buy an HD7xxx or GTX6xx (when they come out) that meets or exceeds the performance of an HD6870.
There are quite a few games that are fun to play and run on older, or lower performing graphics (Deus Ex #1, Sam & Max etc) but I'd play a DEMO first before buying.
There are TWO things to consider when purchasing a power supply:
#1. Overall Wattage (use an online calculator)
#2. The AMPS used by the graphics card (+12V rail or combined rails)
Let's say you bought a graphics card (you need to Google the AMPS) and it required 32Amps, and the online calculator said you need at least a 550Watt PSU.
I recommend at least a 650Watt PSU that supplies at least 40Amps on the +12V rail (or combined rail).