Is this a new CD? Some copy protection features disable playing on a computer. Check the CD back and booklet for details.
There was a neat story with this. Music companies wanted to keep their disks from being read on a PC and Phillips and Sony refulsed to give those disks the official "Compact Disk" stamp because they were going outside the CD specifications. Don't recall ever seeing the outcome of this, but it looks like you may have one of those disks.