Troubleshooting is going into detail and excluding all the things that can't be the reason for the problem. That way you will end up with very few reasons or even just one reason. That way the problem can be narrowed down to find a solution.
In your case if it's neither high CPU usage or RAM, then there is a problem with either Limewire or Java.
One thing that shouldn't hurt trying is Uninstalling Java using Add/Remove programs and then reinstalling the newest version. This should have no ill effect even if it doesn't help, and then we can exclude Java.
You can download the newest Java here:
http://javadl.sun.com/webapps/downlo...BundleId=18713
After uninstalling, you should restart your computer before reinstalling.