When you said copying cd's into the computer, did you mean extracting songs from cd's using iTunes, or adding songs from songs you had downlded using Limewire?

I have a suspicion that the songs were on LW's playlist but weren't actually in iTunes' Music Library. So when you deleted the folder of music, it was all the music you had downlded; ie: the LW download folder. The playlist that was being shared was the Limewire playlist.

Or else, you're trying to play the songs from the LW playlist but the songs are actually still in the iTunes music library. In order to share the iTunes music folder with another computer, you need to enable Share options in iTunes Preferences found under the iTunes Edit menu.