What version of Java are you using? Some people have had problems with Java 1.6 0_01. 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

Now reinstall LW & make sure to use the offline installer (after you choose your platform you'll see the option to use the offline installer, within an orange box on the next download page).

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.

Or try the other fixes in that thread (change compatibility, run as administrator).