Are you running both Windows & Norton firewalls? Don't - they'll conflict with each other. Turn off the Windows firewall & double check that Norton's configured to allow LW.
PortForward.com - Free Help Setting up Your Router or Firewall
http://www.gnutellaforums.com/226610-post6.html

Try this version of Java. Use the JRE offline installer & remove your current Java version before you install the new one.
Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11

If that doesn't help, delete LW's preferences folder when LW's properly closed. See point 3 here.
Fixes for LimeWire
This will kill 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.

If you're using a router, can you find out the brand & model number?