well, Your on the right path
Your batt is DEAD! Try removing the batt from other car, and installing in Toyota. If you are using small jumper cabels... Not much power. If a known Batt is installed and still the drop then you have EX draw from starter motor. In this case, a new starter would be needed.
Await your reply
I finally found your answer. Don't know why the web site sent me around in circles for an hour, with 'view your answer' just sending me back to my question.
That voltage drop from the other car's battery was what I measured at the Toyota, i.e. at the dead car's end of the cables. I had 12 volts coming in
Sorry I didn't know end of line ended the message. ....12 volts coming in, dropping to 3 or 4 when I turned the Toyota's key. Doesn't that mean the small cables aren't the reason? And might it have made any difference if I'd had the other car's engine on, idling away, when it was supplying battery power? Incidentally the other car is a Toyota Prius (hybrid), I'm using that dinky little auxiliary battery in its trunk.