I doubt that Firefox is the problem I've been running Firefox in the background while playing GW, for years, and I've never had the OP's problem. I'm running version 4 of Firefox now, and I highly recommend you upgrade from any earlier version, if only for the increase in screen real estate.
The background task that's running would probably not be anything as obvious as Firefox anyway. It would more likely be something in the Systray like MSN Messenger, Skype (although Skype causes no problems for me), etc., or one of the annoying "Media Detector" or "computer buddy" thingies that some apps install. Check your Systray (right-hand end of the task bar) and see what's in there. You could stop various things from running to see if the problem stops and then decide whether or not you want the applet to run.