When my 4870 broke i resorted to using my old 1900XTX 512MB.
I was running on a 24" Acer G24 @ 1920 x 1200. I managed to run cod 5 at around low - medium settings i think at playable framerate (but not great). I was using a Core2 Quad Q9550 @ stock and 4gb of ram at the time tho.
Best bet would be to get a better card of some sort.
The big difference there though is the 512mb RAM. 256mb and 1920x1080 is a killer