Go through this, double check that your firewall's configured properly & read the info about internal firewalls within routers & modems... if your device has one, there's a lot of info about enabling UPnP or port forwarding to get around the problem
Connection problems? Check here first!

Has anything changed with your ISP lately? Do this test & see if it works
http://www3.limewire.com:6346

What are your details?

OS(Win XP etc)
LW & Java version (help > about LW & you'll see)
Firewall you're using
Modem/router brand & model
ISP
Connection type (DSL etc)
Where you connect from (home, school etc)
Are you sharing a connection with other computers
Is this your first try with LW