My suggestions would be:
1. Open the Add/Remove control panel & remove all versions of Java.
2. Then reinstall Java using
only the "Offline" installer version here
Java 1.5 (take the JRE)
3. Delete your LW Preferences folder whilst LW is
closed; instructions here:
Point #2 & 3 in Fixes for Limewire (sample image included.)
4. Make sure your computer's software firewall is properly configured to allow LW full access, & also enable UPnP on your modem, else manual forwarding a port; instructions for all of this here
Connection problems? Check here first! (click on link)
5. Reinstall LW using only the "Offline" version from here
http://www.limewire.com/english/content/download.shtml