Transmission not going in reverse after battery drained?

Hi, my van shut off while my wife was driving. The battery and brake lights also came on. The belt is there and not broken.
It's at the mechanic now. He said I need an alternator and transmission, there was no problem prior to the battery draining. I put a battery pack on it to release the vehicle into neutral. It was flatbed-ed.
He told my wife it won't go in reverse and didn't elaborate. I get home from being away tomorrow.

Correct me if I'm wrong. If the voltage is too low (bad alternator) You can't make a proper diagnosis. I questioned if the test/his diagnosis was done with a fully charged battery. I got an eye roll.
I'm disabled with an automotive background & just can't do it at this time.
When the battery drains, I understand all solenoids don't operate properly. Can a transmission be hurt by running it till it died due to a bad alternator? Is there a relearn that can be done?
I feel that he is clueless at this point. Trying to avoid towing to another shop.
Although I'm not at the vehicle. I believe put an alternator in fully charge the battery and I should be good to go.

Thanks for your time and help.

Neil