First of all, I am using a new, highly-recommended external Dell CD Disk Player (does DVD and Bluray too). It plays other CDs just fine, so a mechanical issue with it is not a prime suspect.
I have no problem reading CD-R disks from the same batch. It's the CD-RWs that are giving me the issue.
@Igor - while it is possible that the disks may lose information over time, I am moving this down on the suspect list. The CDs have been stored in a benign climate (no extreme temperatures and no humidity and zero exposure to light even). Also, ALL the CDs (about a dozen of them have the same behavior). I don't think I've tried to read them since I put them away years ago.
@Igor - I'll try the freezer trick. I am interested, what is the logic behind this possibly working?
@Horace - the disks are marked with cryptic names like "Backup B2 JGs" - I'm sure there are (were) JPEGs on them at one point.
I do not see a directory listing when I put them in. It sees them as a blank CD. The options that come up immediately ask about how I want to burn the disk and then it goes on to format them. I sacrificed one disk to this process.
I suspect that the software used to burn the CD-RWs was specific to the computer or drive that I was using at the time. CD-Rs promised compatibility and they delivered. CD_RW is some other format. There may exist software that can do the translation. However, beyond having a strong curiosity as to what may exist on these disks, I have no compelling reason to recover them.
I was hoping for a "low-hanging" fruit solution, but since there does not seem to be one, I will abandon the project.
Thanks for the suggestions.