Before you do anything - question number 1: Is your Henry J equipped with a Delco-Remy or Autolite starter? If it's Delco, Joe's method is a good way to eliminate the starter button (a common failure on Delco equipped Js). I fought with that problem for years. The Delco equipped cars have a larger solenoid which takes a lot of current and often burns up the cheap little starter button. If the car is Autolite, and still wired as original, then you need to take the car out of gear, set the parking brake and then ground the terminal on the solenoid to see if the starter spins. That's the main difference - Delco starter button circuits apply 6 volts to the solenoid, Autolite starter button circuits ground the solenoid.
In either case, if the starter spins when you do this, the problem is your starter button or the wiring to it. The Delco units use 10 gauge wires from the starter button to the solenoid, and they need it! Autolite has a 16 gauge wire from button to solenoid.
Here's a Delco unit -
and here's the Autolite
Not the same at all. Different starter buttons and different wiring.
If your car is a '51 or a '52 Vagabond, it will have Autolite. The '52-'54 Corsairs had Delco but there were some rare cases where the later cars had Autolite.
For years NAPA carried the starter button for the Delco units but not any more. I found a good sub at my local Fleetfarm in the Auto department, part number BWD Automotive UN28760. You can also get one at
www.autorewire.comThe Delco style can be used in the Autolite equipped cars. Simply ground one terminal and connect the other one to the wire that goes to the starter solenoid. The Autolite style cannot be used in the Delco equipped cars - too weak of material and only has one terminal as it just grounds the wire through the switch to the dash.