from the very small amount of information provided, (read: none - not helpful at all) I will try to divine what your problem is. I will also be guessing a bit about how LimeWire does some things heh. I will also assume you meant to type past the download, or "after"

While LimeWire downloads a song, the incomplete file has a name that tells LimeWire it is incomplete. SOmething like incomplete0001-nameOfSong.mp3

If you use LimeWire's player to preview a song as you download, you are listening to incomplete0001-nameOfSong.mp3. If the download finishes, it is renamed to nameOfSong.mp3, so when you press play in the LimeWire player again, it can't find incomplete0001-nameOfSong.mp3, so nothing plays. Just find the song in your library (in the library tab) and get it to play from there. Just do something to "reload" the song in the player, so the player knows about the new name.