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

If that doesn't help, try deleting the preferences folder when LW's properly closed (points 2 & 3 below)
Fixes for LimeWire

If you want to reinstall LW, use the offline installer
http://www.limewire.com/english/content/download.shtml