I have some songs that I downloaded in MP3 format which seemed fine and clear at first, but now I play them and there are pops and squeaks appearing. Just like good old-fashioned vinyl.
Can your music playing software affect the file? I'm using a version of Power DVD which was on the machine at purchase. And I've converted them to 128 kbps CD quality through Replay Converter.

Problem solved! Power DVD, although it opens music files, doesn't really handle them well. It's designed to play DVDs - well, no kidding.
Different music programs were recommended at work as an alternative. Winamp was not really what I wanted, and Gom, which is supposedly able to play anything, wouldn't play songs in WMA format. I've settled on ZOOM:
http://www.inmatrix.com/
I installed it, dragged a song over, and straight away I got sound. Can't get better than that.