Do the songs play during preview (while you're downloading them)? Have you tried playing the songs with another player & if so, do they play ok?

The LW player's awful really...you're better off using another player
But, if you really like the player & want to keep using it, try this:
Delete LW's preferences folder when LW's properly closed. See point 3 here & also point 2 if you've used older versions of LW in the past (there could be a folder in either location).
Fixes for LimeWire
This will kill all of your settings within options, you'll have to go back through afterwards & reset things. If you're not sure of your settings, go through LW's tools > options & write them all down, so that you can reset things later.