Do this simple test for us. Using your browser go here: http://www3.limewire.com:6346/ The page should say 'Your test worked!'. What happens when you go there?

Can you give us a total desciption of your set up:
1. Do you share a connection such as on a network or share a router?
2. Do you attempt to use other p2p programs simultaneously?
4. Connection type? (eg: dialup, broadband, cable, etc.)
5. Modem & router brand name & model numbers?
6. Where are you trying to connect from (home, school, work, etc.)?
7. What version of Limewire (LW) & Java do you have? (Go to LW's menu Help>About LW...) Will show both LW & Java version.

Try deleting your LW Preferences folder whilst LW is closed; instructions here: Fixes for Limewire