At both home (not the same PC as my other recent post) and work, I have CD-RW
drives that originally worked properly. Now both of them work fine for
reading CDs, but when I try to burn them I get an error message to the effect
that the software can't find a CD writer (even though upon inserting blank
media I get the popup acknowledging that and asking me what I want Windows to
do).

I've tried auto-updating the drivers via Control Panel-->Hardware, but it
says I already have the most recent ones.
I've tried different brands of media, and they all work on other PCs.
I've also tried a few different software options (XP's Explorer, Real, WMP).
XP Home at home, and Pro at work, if that matters.