Are you using the online installation of LW? Lots of people have trouble with that - you're better off using the offline Have you installed the Java update yet?

Try this way:
Install the latest JRE using the offline installer here
http://java.sun.com/javase/downloads/index.jsp
Make sure you've got rid of any old versions, then install the update. Reboot your computer.

Now install LW using it's offline installer.
http://www.limewire.com/english/content/download.shtml

See if that's any better!