Welcome to the forum
I will assume no start means starter motor doesn't turn the engine, because of what you have tried.
The shifter switch for the starter motor is on the transmission, not the gear shift.
Black box on drivers side behind shift linkage
It is called transmission range sensor, Google it
Make sure its plug is tight and it is plastic so make sure it isn't broken
Ranger 4cyl didn't get PATS(passive anti-theft system) until 2001, and I think only in the 2.3l Duratec models.
And you would have a flashing anti-theft light if it was a PATS issue and you didn't mention that, which you would have if it was there, lol.
So assume this is an electrical issue.
In the engine fuse box will be the Starter Relay, when you turn the key to START the ignition switch under the steering column sends 12volts to the transmission range sensor, if it is in Park then that 12volts goes to the starter relay, which wil "click" closed and send another 12volts from 50amp fuse to the starter motor/solenoid, and starter motor will start spinning
Ignition switch-------------transmission range sensor---------starter relay-------starter motor
The 20 minute thing is odd, so maybe dealer or some one added an anti-theft system, if you have keyless entry then that is possible, and they do reset after a certain time.
So try unlocking and locking the door with the key fob if you have one