Remove your old version of Java (add/remove programs) & reinstall JRE using the offline installer
http://java.sun.com/javase/downloads/index.jsp

Now reinstall LW using it's offline installer
http://www.limewire.com/english/content/download.shtml

If that doesn't fix it, try deleting the LW preferences folder (points 2 & 3 below)
Fixes for LimeWire