Are you sure you're logged in with administator priviledges?

Normally reinstalling LW will remove the previous version of LW. And the normal way to uninstall LW without the reinstallation is by going to the Start menu -> Programs > LW > Uninstall.

To fix the problem you had, try steps 1, 2, 3 & 5 here Fixes for Limewire

Oh I forgot to mention, use the Control-alt-del keys to bring up Process Manager & ensure there is no LW listed. If yes, force it to quit.