Go to Start menu -> Programs -> LW & see if the programs starts from there. Or better still, go directly to the program folder & see if you can open it directly. If it does open, then replace your old LW shortcuts with new ones. Shortcuts do have a tendency to become corrupt.

Otherwise, try deleting your LW Preferences folder whilst LW is closed; instructions here: Point #2 & 3 in Fixes for Limewire (sample image included at bottom of page.)

If still a problem, remove all your java versions & install Java 1.5_11 see link in point #1 in Fixes for Limewire.