Try this

First, install Java. Use the JRE offline installer. Remove any old Java versions before installing the new one.
http://java.sun.com/javase/downloads/index.jsp

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

If that doesn't work...try using the 'other' installer & see if that's any better.
Installing using the 'other' installer