First of all install Java. Use the JRE offline installer here. Remove your current Java version before you install the new one.
http://java.sun.com/javase/downloads/index_jdk5.jsp

Once that's done, delete LW's preferences folder. See point 3 here. If you've used much older versions of LW, you could have a folder in point 2's location as well...so check both.
Fixes for LimeWire

Last of all, reinstall LW & make sure to use the offline installer (not the recommended one).
http://www.limewire.com/english/content/download.shtml