Have you configured your firewalls?
http://www.limewire.com/english/content/firewalls.shtml
Is your Java up to date?
Java 1.5 (take the JRE)
Which version of LW are you using?
Do this simple test for us. Using your browser go here:
http://www3.limewire.com:6346/ The page should say ‘Test Page was a Success’. What happens when you go there?
How is your firewall setting setup? (Tools>Options>Advanced>Firewalls)