Well, I have had time to explore further, and I have arrived at the following TENTATIVE conclusions:
1) at least in my case, this was NOT a problem of a bad drive (i.e., one that could not write a CD or DVD); nor was it a problem of a bad CD (although it might possibly involve only CD-R discs; haven't been able to test it on any others);
2) it is possible to burn a CD via this drive - with no apparent problems - using CD- or (for a DVD drive) DVD-burning software (I used Nero);
3) the problem, since it affected multiple drives on the same system, and only when writing using the CD-burning wizard in Windows XP, seems to be a software problem in Windows XP (and perhaps other versions); since I am running SP2, I assume that it might have been "imported" in either SP2 or some more recent hotfix, since things worked OK on (one of) these drives a few months ago (when I last used it, and only had the one drive); it seems to me that this problem still needs fixing, although the other method permits a workaround (assuming you have appropriate alternative software); the problem also might affect or otherwise interact with use of such products as DirectCD or InCD, which allow use of the drive in a way very similar to the CD-Writing wizard (i.e., much like a hard disk); I haven't had a chance to try those since this problem arose (although DirectCD certainly worked for me a few months ago), so I can't reach any definitive conclusion about them;
4) this does not mean that this explains all the various cases of this (or similar) errors reported here (or elsewhere); for many of these, registry fixes or XP Services configuration fixes (as has been mentioned here and in various Microsoft Knowledgebase articles) seem appropriate and helpful; in other cases, drivers and or drives might, in fact, be damaged, misconfigured, or otherwise non-functional;
5) finally, I just note that, after encountering this problem initially, I tried to follow various fixes posted in various places; although none of them solved my problem (except for the complete workaround mentioned above), they did seem to cause other flavors of this problem (drive not recognized as readable, service not configured, etc.) to arise, which then had to be fixed. I don't know if that was just my own blundering incompetence in attempting the various suggested fixes, or if, in fact, some of them inevitably have risky side-effects (conceivably only in the presence of whatever undiagnosed error started this whole chain of annoyances).