Try these things in this order:
1. Remove all Java versions using the add/remove control panel.
2. Install Java using the OFFLINE java installer: JRE 5.11 offline version
Archive: Download Java 2 Platform Standard Edition (J2SE) 5.0 Update 11 (Java 1.5 JRE is the final java version compatible with Windows ME.
3. Run this utility:
Crap Cleaner
4. Try deleting your LW Preferences folder whilst LW is
closed; instructions here:
Point #2 & 3 in Fixes for Limewire (sample image included at bottom of page.)
5. Download and install this version of LW:
http://www9.limewire.com/download/LimeWireWin-full.exe