Reinstall both LW & Java using ONLY the "Offline" installers. You might be best removing your Java versions presently installed.
Java 1.5 (take the JRE) & install "offline" Java 1st. Then the "offline" version of LW
http://www.limewire.com/english/content/download.shtml
See how it goes, if still no good, try steps 2, 3 & 5 here
Fixes for Limewire