Are you launching songs from the media player(s) or from within LW's library?

Try disabling McAfee's firewall. Turn on the Windows firewall & configure it to allow LW. Now download a file & see if the same thing happens. Sometimes, if a firewall's really aggressive it can lead to some corruption of files.

Have you tried any other p2p apps & if so, does the same thing happen? If you like, give BearShare or Phex a try & see how they go.
Get Phex - PhexWiki

If you want to try BearShare, use the version mentioned here. You'll need to use BearStart as well...there are links for download within this thread.
BearShare has been sabotaged.