OK, I found an "archive" version of the site I urgently need to download.
HTTrack downloaded it nice and fast and told me when it was finished. If (!)
memory serves me correctly, at that moment I was able to open and surf the
archive normally, but since then all it does is give me an endless series of
folders to open till I get to the webpage I want. The webpages don't have
their original names but computerese like "_", "__", "_java&", "f-4," "f-5",
"f-7-29d6a" etc. Maybe this is normal and I'm misremembering it from
yesterday, but I'd think the program would do it faster than going through
"Computer" directories in Windows?
I'm extremely grateful for HTTrack! Thank you, HTTrack! Nothing else has
worked at all. Everything else that promises to (e.g. IE "Save as type Web
archive single file", Cyotek Webcopy) ONLY copies the page that's showing. If
anybody can guide me how to get those (or other utilities) to work as backup,
I'll be double grateful.

Incidentally the four-character captcha-type code doesn't show for me. I have
to click to open it in a new tab.