I downloaded limewire and it is on my desktop, but when i try to run it nothing comes up. I have tried redownloading it, but it still isnt working

Do you mean that you can't open LW? Try the tips here: http://www.gnutellaforums.com/331559-post2.html

Opening is not a problem, it won't connect to the internet.
N.B. I'm on a Mac OSX 10.5.6

Ok. Do you have LW 4 or LW 5?

Try the tips here (there are links for Mac users): If LW Will Not Connect

If you're still stuck, please post back with your system details as shown in the help thread

Thread moved to OS X section just because there are so few Mac users here & if there's a Mac problem, it's better there - where the Mac users will see it.