Well, this is probably bad news, but you must ask your IT department wether they are blocking P2P with a firewall or something.
Alternatively, you can ask them if they have a firewall up (they most likely do) and then ask them if port 6346 (the one LW is using by default) is blocked.
If it is, then ask for a non-blocked port (try and do that in, uh, a discreet manner. You don't wanna seem like some hacker who wants to take over the cyber-world from his campus
). If they give you one, then go put that in LW (Limewire->Preferences->Advanced)