It could be a couple things. If your using the LW player try using a different one. In LW go to Tools>Options>Player, untick the box and click apply. You may need to restart LW for the changes to take affect. Now songs should play in your default player. The LW player isn't very good.
It could also be a codec problem. You may want to try
VLC media player, it has the codecs built in and will play most file types. More info on codecs and other players in this thread:
CODECs list for Movies /Alternate players / Video help forums.
Or it might be that the songs you've downloaded are fake. The network is full of them, but you can learn to avoid them and find good ones.
See:
Recognising Fake files
And for tips on finding good files, see:
How to find music