My solution was to install Slackware 11.0, which as far as I can tell, is the last slackware release to still use boot floppies. In the course of the install, I discovered that one of my hard drives wasn't reading. I replaced it, and that ended the problem. I don't know what that would have to do with finding the CD drive in the bios, but there it is.
It was the hard drive holding the / (root) partition, not the one holding my special data, a lousy 20 GB, so it was no big loss. I replaced it with an old 10 GB hard drive, which holds the / partition just as well as the 20 GB.