Check that your Norton firewall's configured to allow LW. You could even remove the current rules & reconfigure it.
PortForward.com - Free Help Setting up Your Router or Firewall
http://www.gnutellaforums.com/226610-post6.html

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 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.

Who is your ISP (who do you pay for your internet)?
What's the brand & model of your modem/router? If there's nothing showing on top, look underneath.

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