You need to read through this, it has heaps of info about connection problems
Connection problems? Check here first!

Make sure that your firewall's still set up to allow LW access. Do this test & see what happens http://www3.limewire.com:6346

Did anything change (new hardware, new firewall, new ISP or change of plan etc) before your LW stopped connecting? Are you using UPnP or port forwarding through your modem/router?
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