OK lets try the easy solution first. Since that link gives an error it is most likely blocked

In limewire go to tools>options>firewall config and change the ports into a number beween 50000 and 60000. If the first one doesn't work then try a few more. If you are using UPnP just change the listening port. If you are using Port forwarding then change that number to the same as listening port. You will of course need to forward that port in the router if using port forwarding (Both TCP and UDP, incoming and outgoing)

About the firewall. You really should use one. You are leaving your PC open to attack from the internet. In both the "Getting started" and "Tips and tricks" forum there is a thread called "Antivirus and so on". Download the Sygate firewall (Freeware). It's really good and easy to configure.

Just allow Limewire.exe, the go to advanced and open the port for Limewire (Both TCP and UDP, incoming and outgoing).