Sorry for a (very!) late reply to your original question. Just in case you haven't managed to resolve your problem (and I apologise if this sounds like a daft query but...) are you playing the no-CD version of the game or is the CD present?
One reason for no music playing when all other sounds do (e.g. gun shots, death grunts, etc) is simply because you're playing the no-CD version of the game - could you confirm so we can rule this possibility out?