It worked! Using ISOBuster, I was able to get my files off of the CD. ISOBuster ALSO indicated the files were "open session". Subsequently, a neighborly "expert" determined that the CD's had not been finalized.

Why and how? My neighbor RECREATED my previous environment, Win 98 Se 2nd edition and Plextor, Adaptec, etc. He was able to download my backup CD's to an exernal HD. Indeed, my CD drive was controled through Plextor 2000. P-2000 also had Adaptec burner software bundled with it and was my burner software. It did not finalize a CD when saving to it. That was why I was able to use the same CD-R to write additional files to or to update current files and resave. If the CD had been finalized, I wouldn't have been able to do so, and I wouldn't have had to go through all this trouble.

Thanks everyone for their input and to PATIO for turning me on to ISOBuster. A GREAT deal for @$30.00.A CD that is finalised cannot be written to unless it is a re-writeable and is erased...
Depending on the software used every time you burn before doing so you need to check whether session burning or finalising is switched on depending on what you want...
Session burning means the CD is not finalised until you do so.I REALIZE that now. It is just like a regular music CD burner/player. You can record on one side (burner), but can't play it on the other side (playback) unless the CD is finalized after recording. Again, thanks, Patio! You're more than Welcome and stop by anytime...