So you know the engine is not stuck.
Sometimes the ignition switch will lose contact from sitting from oxidation. Maybe that is why you do not get anything when you turn the key.
When you jump the starter you need to jump the battery post to the solenoid post otherwise, like you said, the starter will spin but not engage the solenoid.
Also, if the car has been sitting for many years, as stated, just throwing a battery in it and trying to start it can cause severe damage to the engine.
At the very least, you should pull the plugs and squirt some oil/Marvel Mystery oil or some other lubricant into the cylinders and let them soak for a few days. Then, with the plugs out, turn the engine over by hand.
These flatheads are notorious for the valves getting stuck from sitting, too, so lubing everything before turning it over is a good idea. If some of the valves are stuck you may need to pull the head.
I would disconnect the fuel pump line to the gas tank (and carb) so you do not pull any dirt into the pump and carb.
You will most likely need to clean the points, too, as they oxidize from sitting and will not spark.
The best thing to practice while resurrecting a car that has sat for a long time is - PATIENCE!!!!