You don't have to disable the firewall...just configure it so it allows LW

What version of Java are you using? Try this version. 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

If that doesn't help, 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.
LimeWire Pref Folder in Vista

If it's still not opening, try changing compatibility (point 5 in the 'fixes' thread) to Windows 2000 or NT. If you're using Vista, run in compatibility mode for XP.

If you decide to reinstall LW, make sure to use the offline installer (when you click to download LW, the download box will pop up. Cancel that & you'll see an option to download the offline installer).