Thanks, everybody!
I took the first clues and called Soooby Dealer Parts. Cable bundle - $130 something. New starter was north of $500. The value of the car is somewhere in the middle.
Went to the dead car, which had been rained on. Tried to crank, and it just clicked. BUT the key clue emerged. The slightly wet negative post on the battery steamed little wisps of vapor. ahHah. Bad connection plus lotsa amps equals heat. The bolt was as tight as it would go - so rummaged for a metal screw and drove it into the crevice in the clamp between the clamp and the battery post. The metal screw bit into the clamp and the post.
Fired right up. Bingo.
THanks to all for their thoughts. Very helpful.
k:)