I have had this touble with both audio and video CD's. Two possible solutions.

1. It is something to do with an encoding file on the CD which tells the CD player where it comes from.

We bought a very cheap CD player here in China and it plays all the knock off video and audio CD's. However the more expensive CD player in my PC is a bit more discerning and can tell which is a knock off and refuses to play them.

Sometimes if you have burnt a CD then this file gets stuffed up or is missing.

2. Wipe the disc clean using soft tissue. This sometimes works as a fingure smudge or scratch can confuse the set up for the disc. Some players are more sensative to mucky discs.