It probably isn't working on the campus Wifi because you have to agree to the network Terms of Service. Try opening a webpage in the browser - I'll bet it redirects you to something you have to agree to before you can use the network. After agreeing GTalk will probably work (at least up to the point the system times out and you have to click the agreement again).
The other possibility is that they are blocking the ports that GTalk works over. If that is the case - well you could try talking to campus IT and see if there is a work around or exception list. Beyond that the only solution I can think of that might work is setting up a VPN to get outside of the school network.