If you wnt to clean the player.............Go to radio shack and buy a small bottle of electronics cleaner. It will have a small straw on the can like WD40. Shove that little straw in the deck and spray it. It dries quickly and is made for electronics so don't worry. Spray left , right . up and down. I'm telling you it eveporates quickly and clean. It's also non conductive - no worries. Can clean your computer keyboard, anything electronic.
The rason it's not playing is something called "sampling rate". Car stereos can be 8:1 or maybe 16:1. Home CD players are much higher and of better quality when reading CD's. MAny home CD players are 32:1 maybe more.
Sampling is when it looks at the music and see a difference in what it thought was right and a small error. It says how many were the same and how many were different at the sample rate. Lets say its 8:1. It looks at 8 "bits" in the stream. 5 were one way and you hit some dirt / scratch and 3 were another. 5 is better than 3 , play the stream using the 5. If the 5 bits were the dirt , than it plays that b/c 5 is greater than 3.
Better sample rate ,better chance that the "music" will be the higher correct data to play and hence higher sensitivity to the music data stream.
See if your computer can read it and burn a new one for the car. They are not indestructable you know. What your experienceing is normal and I bet even after cleaning you will still have the same problem. Find something or someones computer that will play them and then burn another.