After some delay in dealing with this... I was able to fix the problem... and now my Pinto drives again!
I put in a newer battery, and the starter still wouldn't turn over. Also had some small flames on the side of the starter near the positive cable -- the arcing had ignited oil that was on the starter, from oil leaking from the valve cover, and possibly the oil pan gasket -- the oil had coated the positive connector on the starter, interfering with the electrical connection.
I disconnected the battery, jacked the car up and removed the positive cable from the starter, as well as the connector strip. I then sprayed the connector with carb cleaner, wiping it super clean, and reconnected it.
Reconnected the battery, and she turned over. poured a little gas down the carb (she'd been sitting for a couple years or more) and she started up.
Now I have to learn to get rid of the oil leaks. But at least she runs.