Are you using the LW player or another player? The LW player is horrible, but if you really want to use it & it's not working...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.

Has this just started happening (ie have download played ok in the past)? Do CDs play ok on your computer? Are you sure that you're downloading real music files (there are lots of bogus files around)? Check the extension, file size, bitrate etc & make sure that everything looks ok.