Jim Tittsler pointed me in the right direction when he said it might be "overzealous" anti-virus software.
Sure enough, when I turned off AutoProtect in Norton AV, the floppy and CD drives became accessible again. Sheesh.
There is a document (the ID is 2003050715532006) on the Symantec site that says the problem has a "variety of causes" and "can be caused by a timing conflict between one of the features of Norton AntiVirus and another software program that loads on startup."
Nero software, in particular inCD is mentioned, and Symantec suggests upgrading one's Nero software.
I dunno, after being a loyal Norton user for years, in the past year or two I've been having increasing problems with their products. Time to investigate other options?