Well, it had done this before. So I booted the tablet into recovery mode and reset to factory defaults.
Sadly, the internal SD card still wouldn't mount. Grumble.
Well, let's go browsing on-line for help. Ok, here's someone who rooted their tablet and rebuilt the mount code for the SD card. I can try that.
So I rooted the tablet. And then I tried to mount a small partition on the SD card following the instructions, but they didn't work as given. Of course, they were for a different tablet.
Let's try this instead.
The tablet is now a brick. It cannot even be booted into recovery mode.
Ah, well. I had expected that I was about to buy her a new tablet anyway, so this was no great surprise. (I wouldn't have been experimenting with rooting it if I'd thought anything else was going to revive it at this point.)
The new tablet is faster and cheaper than the one I bought last Christmas.
This is not a surprise either. :)