I can't guarantee that a cleaning disc will solve your problems, but I swear by them myself. I bought one for $14 on a recommendation from a friend when my DVD player stopped reading discs. Worked like a charm, and we still have that same DVD player many years later. I was so impressed that I ran it through my CD players, which were both several years old, and I was amazed at how much clearer the sound was -it was like having a new CD player. Now I run the cleaner through every month or two, just as a preventative measure. The instructions that come with it say to use the cleaner after every 10 hours of CD player usage, but that seems a bit unnecessary to me.
I've heard people say that these cleaning discs can damage the surface of the laser lens, but I've never had that problem.
Of course, it could be that your CD player has puked bigtime for any other number of reasons, but for $14 you can't really go wrong, IMO.