The connection tab is not shown by default - you need to go to the 'View' menu item and tick 'connections'.

You must be connected to the internet before you start LimeWire.

Havr you tried the telnet test? - telnet router4.limewire.com 6346 - you should get a response of "Gnutella OK".

What operating system do have? Java version? LimeWire version? Do you have a firewall/router? what type of internet conenction do you have?

Mark