I'm thinking firewall is the problem. BTW Turning the firewall off is not a good idea.

Do you get any connection attemts in Limewire ? Press connections tab to see (if you don't have that then go to view>Show/Hide>Connections)

First of all... Are you sure that you have only The Norton Firewall enabled ? (XP Firewall or any other disabled.) It's really important to only have one firewall

Second... Have you made new exeptions for Limewire in your Firewall exceptions ? If not then delete the old exceptions and make new ones.

You could try forwarding ports in your firewall
In Limewire go to Tools>Options>Advanced>Firewall config and choose to forward a port (recommended one between 49152 and 65535) and then set the exact same port as your listening port. Press apply then OK.
Then make exceptions for that port in The Norton Firewall (Both TCP and UDP)

Hope this helps

If it doesn't then

You could also check with your ISP if they have some kind of firewall there that you go through