Did you check if the ignition switch, which is located under the steering column, had full travel before installing the new key cylinder?
The actual ignition switch is a slide switch under the steering column.
The key switch has a metal rod that pushes the slider in the ignition switch into it's various positions when key is rotated.
So remove key cylinder again, and use a screw driver to rotate the key switch to START and then to ACC. to make sure ignition switch has full travel.
Ford changed the key cylinders through out the years, you may have been given one that is incorrect, for the female side.
Since you don't have a history with this vehicle("I recently traded for a 98 Ranger") it may not have a '98 key switch, especially if there was a problem with it when you got it.
Previous owner may have had a problem and just got whole key switch from wrecking yard.