That little red button is telling you there is something seriously wrong David. I would quit pushing it until the problem is fixed.
It could be a simple capacitor or relay in the control box. If you are getting any water at all, the pump is starting indicating the start cap is still ok. The relay being bad will keep the motor from coming out of start and will trip the overload, but as many times as you have indicated pushing the buttom, I would think the start cap would have blown long before now.
You indicated the pump may be from the 1978 era. That's a long time for a submersible pump. I'm thinking your up against a big repair bill to replace that 27 year old pump.
One other thing it could be since you didn't mention horsepower, if it has a run capacitor (the metal one, silver in color) could also be bad, making the overload protector trip. If you want to spend the money and not call a serviceman, you could buy the new parts or a new box. If that don't do it, it's down the well or bad wiring going to the well.
If you bought a new box from me and it didn't work, and had me install a new pump, I would be installing a 2wire pump which doesn't require a control box and since we don't allow returns on electrical or electronic parts you would be stuck with a new box.
bob...
