Did you preview the songs as they were downloading? There's a chance that you've downloaded some junk files. Try playing them from your saved folder, outside of LW. Go to your LW library, click on Saved files & then click Explore. Once the saved folder opens, try to play the files & try using a couple of different players.

Check out the tips here
How to find music

If the files play ok from the saved folder, delete LW's preferences folder when LW's closed. See point 3 below. This will kill all of your settings within options, you'll have to go back through & reset things afterwards.
Fixes for LimeWire

See if that makes a difference, things might launch properly now!