I think the latter 2 posters (shaun.warren & Agkinara_13) should maybe look at the Connection Problems section of the forum.

Start off with some simple tests:

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?

If you can't reach that page then it means your port 6346 is being blocked. This could be due to a firewall, a connection device like a modem/router, or your isp or line managers somewhere along the line. You could try a different port no. & enter it in the Listening port section of the Firewall section of: LW's menu Tools>Options>Advanced>Firewalls.
Mac users will find this under your Preferences tab. Some other ports to try are: 3500, 1203, 20282, 80 (latter as a last resort!) Don't forget to press apply button after making any changes. Go to menu, File>Connect.

Another thing you can try is delete your LW Preferences folder whilst LW is closed; instructions here: Fixes for Limewire (make a note of your settings under Tools>Options before you do this b/c you'll need to reset them next time you open LW!) Let's hope your isp's are not using programs to filter or block p2p sharing or specifically LW.