Make sure you have the latest ATI drivers(new ones every month), game updates(there is a large-ass patch for CoH). Sound, chipset driver and windows updates also matter. Also do a virus scan, adware scan and a spyware scan. Then do a registy cleaning with CCleaner and then defrag. All of those should help.
I have a 4850 with 4GB RAM with a Q6600 @ 3.0Ghz and the game runs on max just fine at 1650x1050. You should be fine too. But I am using Vista 32 not 64. So that could be an issue.
Honestly I would put my money on the video drivers and the game updates. Try uninstalling the game and reinstalling then patching. Also try uninstall the drivers, rebooting, and reinstalling the newest ones.