I've had excellent results from a Meguiar's product you can (or could years ago) buy at NAPA or Schuck's-- there's a plastic cleaner, and a plastic polish, for boat and airplane windshields, etc. The cleaner is more abrasive than the polish but neither adds scratches in my experience. Total investment $20 and I have enough to do 1,000,067 CDs / DVDs. Keys to this method:
Use towels that are 100% cotton- no polyester thread, no paper towels, no towels that have ever had dirt on them.
Put the disc on something sturdy with a thin 100% cotton towel under it. You will be "elbow greasing" the scratches out, you need to support the disc, or you will snap it in two.
Good luck.
Once you make your cherished CD playable again, burn a copy of it for the car so you don't add damage to it in an environment where you're hard pressed to hear the diff between the original and the copy.
Use towels that are 100% cotton- no polyester thread, no paper towels, no towels that have ever had dirt on them.
Put the disc on something sturdy with a thin 100% cotton towel under it. You will be "elbow greasing" the scratches out, you need to support the disc, or you will snap it in two.
Good luck.
Once you make your cherished CD playable again, burn a copy of it for the car so you don't add damage to it in an environment where you're hard pressed to hear the diff between the original and the copy.