First of all, update your Java. Some people have had problems with the latest Java update, so try this version. Download the offline installer & remove your current Java version(s) before you install this one.
Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11

Are you downloading LW from the official site? The latest version of LW is 4.14.10, 4.12.6 is quite old.
When you reinstall LW but make sure to use the offline installer...less chance of a corrupted installation When you click to download LW & a dialog box pops up asking if you want to save the file, cancel that. Now you'll see the option to download the offline installer.
Lime Wire » Download LimeWire

If you're still having problems, 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.