Did you get an error message (with a number?) when the Java install failed?

Try again to reinstall the JRE & make sure that you use the offline installer
http://java.sun.com/javase/downloads/index.jsp

or you could try the Java beta but you'll have to remove all old Java versions first
http://java.sun.com/javase/downloads/ea.jsp

After installing Java (providing it works) reinstall LW using it's offline installer
http://www.limewire.com/english/content/download.shtml