So you had LW before & it was working? If yes, then try deleting your LW Preferences folder whilst LW is closed; instructions here:
Fixes for Limewire
Otherwise if this is your 1st use of LW, can you tell us your connection devices brand & model no.'s. Who is your ISP provider?
Did you do this test? Using your browser go here:
http://www3.limewire.com:6346/ The page should say 'Your test worked!'. What happens when you go there?
Another option is to change the port LW uses. Go to LW's menu bar, Tools>Options>Advanced>Firewalls, & change the listening port from 6346 to another like these 1111, 3500, 4008, 1203, 80, 20282, 10000, 443, 40475.
Ports can be blocked due to ISP blocking, connection devices, etc. Different solutions to each.