Go here with your browser, see if the test works
http://www3.limewire.com:6346
If the test doesn't work, it means that LW's default port is blocked.

Make sure that any software firewall (remember, only use 1) is configured properly
Firewall setup

If the school is blocking p2p (lots do, because p2p uses a lot of bandwidth) then there's not a lot you can do. If proxies aren't working it doesn't sound too promising. You'll need to talk to the school's computer admin & find out what the policy on p2p use is.