Try a CD Lens Cleaner, find and install what FIRMWARE you can for the drive, then replace the drive.
It is possible you created those CDs with DLA or DirectCD or other, but you didn't write such. Those disks will vanish until you install DLA or what you used to create them.
In closing, any CD you want to backup, if you use DLA/InCD/DirectCD/FileCD or other CD as a drive software, you will someday learn why I don't use that method.
I am having a problem with my CD-RW. I have an HP Cd-Writer 9100i Series. One day all of a sudden my CD-RW just up and stopped reading my burned disks. It can read store bought cd's, just not the ones I burned. (Also same problem with my DVD-Player) Any Audio, Video, or Data cd's that I have burned are now useless. Windows tells me it is a blank disk when I know there is data on it. I have researched the problem on the HP website, Windows website, and the internet in general with no luck. I do what the websites say, but it still doesn't work. I have a backup cd of my Windows XP Professional installation cd and I want to re-install my OS. Problem is, it's a no can do because my CD-RW won't read it. (I did have original cd, I like to make copies of my cd's so that if something happens to my original, as in this case) If my OS was to mess up, there is nothing I can do. I have Windows ME setup disk, but it is an upgrade.....I have a burned Windows 98 cd.....which I need to work so that I can verify I have an earlier version. If there is anyone out there that could help, please let me know.