Love to google search keywords of new issues to troubleshoot or just to see how vast a spectrum returns... Did search 'Call Of Duty 4 + ie connectivity issues' to exhaust the idea that it sounds like your local machines security settings might be needing a good reset
here makin' sure Microsoft .NET Framework 1.1 and hotfix are installed prior if this is the chosen route.
Well that search turned up two possible solutions,
one being the router: "at last The first patch will be a Optimized Connection Patch, First the troubleshooting, those of you experiencing connection issues should check your router and make sure the following ports are OPEN:
Port: 3075 UDP
3074 UDP", found in the preceeding link, and the
other mentions everything imaginable also confirming the above.
Unless I am missing something here, there are not too many pc users having the exact same series of events and you're still able to connect to the internet with firefox. If it is not the router or a P2P blocker the game uses, you might need to reset your operating system back to original verbose default security settings first mentioned.