If you don't have Java, LW won't work.
Download the latest JRE offline installer here
http://java.sun.com/javase/downloads/index_jdk5.jsp
Just double check that there's no old Java versions on your comp. If there is, remove it. If there's not then install the JRE.

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