Hello again poppy4,
It worked. After the battery ran down overnight, I plugged it into the power supply in the morning and it booted normally, and is working normally. Thank you for letting me know that this was not a problem particular to my machine. It's still under warranty for a couple of years, but I think I'll wait and see if it happens again. Your "feeling" was the same as mine: the last time my battery ran down, when I restarted it came back to the same screen as when it stopped. Anyway, at least you and your daughter might have a new solution; taking the battery out and putting it back in would seem to be more of a fuss than what I did, unless, of course, you needed to use the machine right away.
Thanks again,
Chas