It sounds bit strange that you cannot browse websites with Firefox. Which version are you using? Did you check your proxy settings in Firefox? I assume you do not use proxy so you shouldn't have defined one in FF options.
As for other games they all need certain ports forwarded on the router (also, as you mentioned, firewall needs to be set properly).
Battlefield Vietnam TCP: 4711,14667,28900 UDP: 15567,15690,4555-4557,23000-23009,27900
Hope this helps, if not, we will need some more details on your problem, like FF version, error message, vista app. logs etc.