I downloaded some songs and at first they started to play. Then out of no where I clicked on a song to play it and it didn't work.. how do i fix this problem?

We will probably requre more details than you have provided.
Things like what version of Limewire are you runnning and what operating system you are using before anyone can give you any sort of definitive answer.
Files should not just stop playing for no apparent reason. Did you install anything else recently that might be infected or causing this problem.

Limewire version 4.16.6 and my operating system is Windows Vista Ultimate

Have you tried going to you folder that you have your songs stored in and double-clicking them or right clicking and telling them to play with whatevermp3 player you have assigned to that file extension?
Sometimes mp3 files are not set to open in iTunes and you can check this by going into the start menu and going through "Default Programs" to check what file extensions are assigned to which application.
Apart from that all I can suggest is for you to un-install and re-install LimeWire and see what happens them.

I think I found the problem.. I think it might be my WMP if thats even the problem. That doens't work either and maybe that has an effect on LW ? IDK but I emailed the guy who set this up with the problems and hopefully he'll be able to fix it