My opinion of cleaning discs is that they are a waste of money and they don't really do a very good job. You will do FAR BETTER (if you feel competent enough) to take the cover off the CD player and clean the laser lens with some isoprop alcohol and a cotton wool bud. Isoprop alcohol is the stuff that comes in the bottle with cleaning discs.
If for example your CD player is used in a house that has smokers, then after a while it is possible for the laser lens to get an accumulation of Nicotine on it, and basically a cleaning disc will not get this off. The method I have described above will give a much more thorough cleaning. JUST REMEMBER TO UNPLUG THE CD PLAYER FROM THE ELECTRIC POINT FIRST!
Or if you don't feel competent enough then,
Have you tried putting the cleaning disc in the other side up and seeing if that makes any difference?
Also try various other cd's to see if the problem is there.
If the discs are scratched then there is a chance that the player will not recognize them and as such mention "NO DISC"