Okay, there are two possibilities. Either something is wrong with your network configuration or a firewall / proxy / your ISP deny you any connection to router4.limewire.com:6346.

In the latter case you can connect by downloading a gnutella.net file ( ftp://whitedragon.dyndns.org/gnutella.net ) and copying into your LimeWire directory (c:\program files\limewire on windows or ~/LimeWire on Linux)