You can't uninstall LW using the add/remove control panel. The normal way to uninstall LW is to go to Start menu > Programs > Limewire>Uninstall. Otherwise, reinstalling LW will uninstall previous copies or versions of LW at the beginning of the installation process.
Personally I'd recommend these steps:
1. Make sure your firewall & modem/router are properly configured to allow LW full access. That means for a router to enable UPnP or if it doesn't have that ability to manually port forward; see
Connection problems? Check here first! (click on link)
2. Install Java using the "Offline" version of LW. Get it here
Java 1.5 (take the JRE)
3. Install the "Offline" version of LW from here
http://www.limewire.com/english/content/download.shtml