“When in the "ON" position, everything on the dash lights up, I can hear the fuel pump and the car draws about 10A. It goes up to about 20A when I try to start the car. I never noticed this before but the climate control, clock and radio turn off when the ignition switch is turned to "start". I assume that is normal.”
Yes that is normal.
As the car has been standing long enough for the shifter to stick, it can also have the starter gear stick to the starter scroll, that the solenoid should push the gear into mesh with the ring gear.
As the bottom of the bell housing is open, moisture condenses up in the top of it, where the starter gear is, so the solenoid just clicks.
I have had this happen to my car here in the tropics.
