Totally reinstall the game, and update to the latest patch. If you can't update to the latest patch, please post the error message you get when you try.
After that, if it still doesn't show any servers, try cycling between the different connection options on the browser, from Internet to LAN to Favorites then back to Internet, and it should do a full refresh and at least show some servers. The browser requires a bit of coaxing, but after a while you should be able to see a full server list.
The other alternative is to download a third-party server browser that support CoD 4, such as XFire or QTracker.