dorald wrote:
About 5 or so years ago, give or take a few, the original hard drive crashed and wouldn’t respond to anything. On the advice of the Apple Support folks, I exchanged that HD for a SSD hard drive and installed a copy of the operating system. ...
How that was accomplished is important.
With those model year iMacs, replacing the HDD with a SSD also removed the HDD's Recovery partition, so ⌘ R would do nothing. The OS would need to have been reinstalled from that Mac's original, grey, System Install DVD or by restoring a Time Machine backup. Either one will re-create the local Recovery partition on that particular model Mac, and ⌘ R would once again function.
Internet Recovery won't work. A 16 year old iMac would be too old to use Internet Recovery. Forget about using any of the ⌥ ⌘ R options. It's ⌘ R or nothing.
For what it's worth it has been my experience that using a wired (USB) or wireless (BT) keyboard doesn't matter — as long as they are Apple keyboards and remain correctly paired with the Mac. ⌘ R works the same either way. Should you eventually conclude it doesn't work then I believe you will need to boot from that Mac's original, grey, System Install DVD.
Other methods may be an option so if you don't get anywhere please write back for suggestions.

This is interesting new information:
-OR- when I do sigh in under my wife’s name and navigate to the “TERMINAL” window and type in “resetpassword”, it doesn’t work as I’d been told.
Because once we are signed in to a User Account we don't use that method to change a login password. But now I'm confused because I had been under the impression you couldn't log into that Mac at all. If you can in fact log into that Mac you ought to use that opportunity to create a TM backup, which could throw a lifeline in the direction of your precious files.