1963 Dodge Dart No Drive

First let me thank all of you who reply to this.
Second this is a long post please read carefully.
I have two questions.
Known information about the car.
1. 1963 Dodge Dart 270 four door.
2. Slant six.
3. Push button automatic transmission.

Details of problem.
1. Started car as normal.
2. With foot on the brakes. Released the parking brake. Released the parking pawl.
3. Tried to push in drive button to no avail.
4. Pushed in reverse button I have reverse.
5. Pushed in 2nd button I have 2nd.
6. Pushed in 1st button I have 1st.

Questions
1. Is the problem just the inside push button mechanism? Or possibly the cables.
2. What is the easiest way to remove the push button mechanism?

I have a 2nd 1963 Dodge Dart with a push button automatic so no worries there.

Thanks again,
Donovan Frasure
Author: Donovan