You shouldn't need to turn all your firewalls off, just configuer them so LW & Java have access: http://www.limewire.com/english/content/firewalls.shtml & Norton at the bottom of that page. An alternative instruction for Norton is: Configuring Norton Internet Security

What might be an issue is your connection devices. Many high speed modems/routers use a type of internal firewall. There's a few types but most common is NAT. Which means you would need to forward a port (open a port) to allow LW access. (If you were using high end games or video conferencing you'd need to open many ports.) The fact you're using a LAN suggests you probably do use a router.
Can you tell us your Modem & router brand name & model numbers?