Which versions are you running (old and new)?

is the new limewire version actually trying to connect?

maybe you have a proxy server setup for your internet connections. check the internet (-explorer) settings for proxy settings and make sure that there is no proxy set. at least none that is set for all connections for HTTP, FTP only should be fine.

make sure the firewall is set to forward all connections on port 6346 to the computer currently running LW. maybe it is forwarding it to the local IP of the older computer only. you might have a different IP with the same username on your new notebook.

hope it helped, good luck

mahalo