Reinstall Java & use this version.
Java SE Downloads - Previous Release - JDK 5
Use the JRE offline installer, remove your current version of Java before installing this one.

If that doesn't fix things, try deleting LW's preferences folder when LW's properly closed. See point 3 below (also point 2, if you've used much 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 it's still not opening, try changing compatibility (point 5 in the 'fixes' thread).

Or reinstall LW & make sure to use the offline installer (not the recommended one). But if you're going to reinstall LW, make sure you've reinstalled Java first.
Lime Wire » Download LimeWire

Dano's too quick today!