Did you use the offline installers for both Java (JRE) & LW? Remove your current Java & try again with the offline installer
http://java.sun.com/javase/downloads/index.jsp http://www.limewire.com/english/content/download.shtml
Try deleting the preferences folder (points 2 & 3 below)
Fixes for LimeWire
Have you installed or updated any antispyware that could be stopping LW from opening? If this is the case, make sure that LW's on the list of exceptions/allowed apps