Try changing your Java version, a few people have had problems connecting with 1.6.0_01. Use this version instead. Download 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

You could also 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.

Have you always seen the firewall icon? Once you're connected again, if you want to try getting rid of the firewall icon, you could try port forwarding. The instructions for your router are here.
PortForward.com - Free Help Setting up Your Router or Firewall