The problem has been fixed. The print server on the printer retains a history of server instances. You can see them if you type the IP of address of the printer into a browser (just as you do when trying to configure a router). The printer server management console will appear. Go into Configuration.
In my case, there were seven or eight of these instances. If glitches happened (they did) tech support would advise to uninstall and reinstall the drivers, and I'd installed, uninstalled, and reinstalled the drivers multiple times over a couple of years. This printer was first used on an XP machine and then on a Windows 7 machine.
After Deleting All of these instances, shutting down the PC, and the printer, and then turning the PC back on and logging in to my desktop, and then turning the printer back on, in that order, the scanner started working again.
Not sure how these defunct print server instances were "clogging" up the works, but they were.
It took three calls to tech support before I reached a tech who suggested to delete those old entries. Lexmark tech support is divided into techs who know the hardware and techs who know the print server software, and if you follow the phone tree prompts you might not get routed to the right kind of tech.