Are you networked with any other computers? Do you have firewalls enacted? If so, which ones?
Have you configured them for LW's access. DAAP will try to find any other computer connected on a lan. And iTunes also has a daap file sharing capability where you can access other people's playlists. So this request is being sent out of your computer & it might be getting snagged by your firewall(s) & even anti-virus/spyware, etc. Which version of Java do you have?

The only alternative I can think of is to try an earlier version. http://www9.limewire.com:82/download/