Is this COD4 single player or on someone sever somewhere? Try the demo single player to eliminate internet issues.
What HDD do you have?
Make sure all of your power management stuff is turned off.
I also have a 5770 and have the COD:modern warfare free demo loaded. I play smoothly it at 1380 at high settings with no such stuttering. I dont have anything loaded to check frame rates, what are you doing for that?