I was having this problem right up until today. I would try to open Limewire and it would looked like it WANTED to open, but wouldn't. What I found out was that my shortcut didn't work anymore. I went to "Search" in the Start menu and did a search for "limewire.jar". Then I clicked on the executable jar file that it found. That opened Limewire right up for me. Then I just right-clicked it and created a shortcut on my desktop. The Limewire Icon still doesn't work, but the shortcut I created does. I have no idea why, but I'm just glad that it's finally freaking working!

I hope that helps someone.