installing
 

I JUST DOWNLOADED LIMEWIRE AND THE ICON ON MY DESKTOP WHEN DOUBLED-CLICKED IT DOES NOTHING

Your problem could cover a multitude of sins. I sometimes wish the forum rules could be relabelled. They are at the top of the forum page, they are less rules and more a help to getting a constructive reply. Have a look at them and come back wth your system details the name of the icon on your desk top and anything else which will might help some one help you.

Other details which might help is what if anything did you pay for Limewire and which version do you have.