I agree I had the same problem and it seems that if your PC has many versions of Java on it these will conflict with Limewire, even though you would think that the latest Java would uninstall the old versions.

So remove all Java programs via Add/Remove programs in Control Panel.
Reboot your PC.
If you have Zonealarm as your Firewall program of choice then also go to Program Control, Programs and remove all traces of Limewire and Java just to clean it up.
Don't worry as they will all reappear once you start the Limewire program.
Start Limewire it will say it needs Java and send you to its site and you can download the latest version and away you go.
Don't know why Java conflicts with Limewire but it does.

Above should work, have fun.