Try some things such as changing LW's compatibility mode to win 2k; see tips here Fixes for Limewire If still not work change your Java version.

Did you configure your firewall so it allows LW full access (advisable not to have 2 active firewalls b/c they can interfere with each other); Firewall configuration instructions (click on link)

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?