If you're using windows XP then ensure you have disabled XP's firewall. Then for Norton check this Configuring Norton Internet Security

Ensure your modem/router has UPnP enabled. Check the UPnP section on this page Connection problems? Check here first! (click on link)
What brand & model of modem/router do you have?

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?