1991 f-250. The key cylinder seems to be starting the truck at the same location it should just powering up the dash, fuel pump. So when I turn it to the power point it starts up and the starter stays engaged.
I've replaced the ignition switch and the key cylinder. Still the same problem. I've ran wires to the solenoid to hot wire it and it cracks up and the starter does not stay engaged.

 

You will probably get more appropriate responses in the forum for your truck, the garage and workshop forum is for discussion of tools and other workshop equipment.
The last truck I had act this way was my 81 E350 box van, the ignition module was fried and it would attempt to crank as soon as the key was on. With the module unplugged it cranked normally, and was fine with a new module.

 

the ignition module Is on the distributor?
That is the part you replaced?

 

What's the history of the truck, has the ignition switch every worked properly?

I'd pull off the small push on wire at the solenoid that energizes the
starter solenoid.

Verify all of the ignition key cylinder positions work.
Rotate the key counter clockwise to accessories.
Does the radio work?
Does the power windows work if you have them?
Does the windshield wipers work?

Rotate the key back clock wise and remove the key.
Verify you can't rotate the steering wheel. Should be locked.

Rotate the key clock wise to the next position Off.
You shouldn't be able to remove the key.
No power to radio or wipers.
Steering wheel can be rotated.

Rotate the key clock wise to On.
Do the dash idiot lights come on?
Do you hear the fuel pump prime.
Does the radio work?
Do the wipers work?

Rotate the key to Start.
Does the ignition switch spring back when you release it from the Start position?

If you don't have all the correct key positions could be you need to move the ignition switch up or down the column to adjust it, or the actuator is not installed in the correct gear tooth in relation to the key cylinder.

Could also be Bubba has done some creative wiring if you bought the truck this way.

 

Just got the truck, the problem started when I made a new key. I try switching back to the old key and it was still there.
All the position work, but the run/ power position on the key cylinder has became the start position.
As soon as I turn it to power it starts and the starter is on the flywheel. Bad news
I've adjusted the ignition switch on the column. No change still power and starter position do the same action, starting the truck.
Tonight I'm going to pull the ignition switch off the column and use a screwdriver to move it. If it works than it is the rod in the column or key cylinder.

 

Here's a picture of the ignition switch contacts. This is for a 88 so I don't know if the 91 has the same wire colors at the switch but the switch terminal layout is the same.

If you remove the ignition switch from the steering column and unplug the electrical connector, manually move the switch position to RUN. You should not have continuity from either BATT terminal to Pin ST shown as circuit 32 a Red/Light Blue wire.

If you don't have continuity your problem is in the wiring.

If you do have continuity the switch is bad.

The Red/Light Blue wire goes to the clutch safety switch on a manual trans. or to the Park/Neutral switch on an automatic. When either switch is closed 12 volts goes to the Starter Solenoid which energizes and the battery passes 12 volts to the starter motor.

 

Everything checked out, it is a short wire in the wire housing! So now I got a new door bell switch in my cap, went old school. Turn the key to power and push the button.