I was having the same exact problem. I then tried Frostwire or whatever it's called and had the same problem. I had tried deleting the preferences folders, same problem. I tried uninstalling and reinstalling Java, same problem. I finally uninstalled every version of Java as there were some old ones in the add/remove programs. I then deleted every Java folder in any Application Data folders and from Program Files.

Then, without installing the latest Java, I reinstalled only Limewire 4.12 pro, and let it install only the Jave that was bundled, 5.x I think. Then Limewire worked fine. So I then tried to upgrade to the latest Java from Java.com. Yep, you guessed it - Limewire wouldn't run anymore. So I uninstalled Java 6.whatever and Limewire works again.

See if that works for you, but LimeWire just does not work if the latest java is installed on my machine.