Update your Java. Use the JRE offline installer & remove any old Java versions before you install the new one.
http://java.sun.com/javase/downloads/index.jsp

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

If you still have trouble, try using the 'other' installer & see if that's any better.
Installing using the 'other' installer