Once again I'm trying to diagnose the kid's '91 244 from 3000 miles away.

Yesterday, the car started and drove fine. Later in the day - a very cold day, 5F after sundown, he went to start the car and only got a click. Lights, blower, other accessories work fine. He saw that the smaller wire on the positive battery terminal had parted, so that's when I got the call. This morning he reattached the smaller red cable (this is from the alternator?) and had a friend there to provide a jump start, but the result was the same - just a click when he hit the key. I had him check the horn, as it's a high current device and a better check of available battery power than just lights - horn gave a healthy blast. Batter cable connections are clean and tight, and the cable to the starter appears OK.

So from afar, what's the consensus - time for a rebuilt starter?