swap the battery out of the other car. don’t waste money buying a battery at this point. re check the connections. both at the battery, and the starter. You mention corrosion. start there. if the other cars battery solves the problem, buy a new battery (for your car) give the old one with the TC. If the battery swap doesnt fix it, then it is up to you to decide how much more you’re going to pour into this for 700 bucks. Do you like this potential purchaser?
btw, it is possible the starter bendix has just frozen up after all this time of inactivity. If the battery and connections are fine, remove the starter, and manipulate the bendix by hand to ensure it moves freely, and spring returns to home.