It's a bad idea to run more than 1 software firewall. Turn off the Windows firewall...it'll conflict with Norton.

Try removing all of Norton's LW rules & then reconfigure the firewall to allow LW.
PortForward.com - Free Help Setting up Your Router or Firewall

Lots of people have had problems when using that latest Java update, try this version instead. Download the JRE offline installer & remove any other Java versions before you install this one.
Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11

Is the router in another room in the house? Even if your connection's wireless but there could still be a firewall within the router that's effecting LW. So we'll need the brand & model.