Here is the correct terminology for your steering column components. The ignition switch is down under the dash and mounted on top of the steering column. It is difficult to access so that the car is difficult to hot wire and steal. You will need to drop the steering column in order to access the switch.
The part that you stick your ignition key into is the ignition lock cylinder. When you rotate your key you turn the internal parts of the lock cylinder. This turns a small plastic gear that engages a small die cast rack. The rack moves down toward the floor and up toward the steering wheel inside your steering column. The rack is connected to a rod that extends down and attaches to the ignition switch down under the dash.
The fact that your ignition key rotates without resistance is not a good sign. Sometimes the die cast rack inside the column breaks. This will require that the entire steering column head will need to be disassembled in order to replace it.
Disconnect your battery. Now rotate your ignition key while looking at the rod that extends down from the column head to the ignition switch. Does the rod move? If it doesn't move, then most likely the problem is in the plastic sector and rack area. The parts are still available from various sources.
I would suggest going to the following websight. www.corvettefaq.com
click on Jim Shea's Steering Papers
click on A & F-Car Steering Papers
depending upon the type of steering column
scroll down to the Standard (non-adjustable) Steering Column Section or scroll down to the Tilt Steering Column Section
You will find several papers and pictures that might be of help in understanding the column and its features.