duck_butter,

Try removing any LW rules & then setting them again within Norton's configuration. These threads might help.
http://www.gnutellaforums.com/226610-post6.html
PortForward.com - Free Help Setting up Your Router or Firewall

If that doesn't help, delete LW's preferences folder when LW's properly closed. See point 3 here & also point 2 if you've used older versions of LW in the past (there could be a folder in either location).
Fixes for LimeWire
This will change all of your settings within options, you'll have to go back through afterwards & reset things. If you're not sure of your settings, go through LW's tools > options & write them all down, so that you can reset things later.

duck-butter & rizo77,

Do this test & see whether it works: http://www3.limewire.com:6346/
If the test doesn't work, in LW tools > options > advanced > firewall config. Change LW's listening port to something in the range of 49152 - 65535 (eg 65000) > apply > ok.

If you're still stuck, please give us your details (duck_butter, sorry for any repeats of what you've already told us).
System details - help us to help you -> Provide these details when you post!!!