Could Something like this work?
This is the first idea that popped into my head. I'm not sure if this is how punch card readers really work but it's a try.
That being said, I'm not sure if this really works at all.
Anyway, a simple explanation might be in order.
When the user approaches the door, he fully inserts a punch card and presses the lever down.
(Assume that the code to open the door is: A=1, B=0, C=0 and D=1. and that the card is as shown in my drawing (i.e. 4 holes in a row; each hole indicating A,B,C,D from left to right))
As he presses the lever down, the metal contacts go through holes A and D of the punch card and make a contact with corresponding metal contacts on the bottom. At this moment, the current from voltage source has a path (and a load) and it will flow through resistors A and D.The digital logic will triger a timer relay which will give user say 5 sec until the user withdraws card and door locks.
In the drawing I said hollow metal contacts, but thinking about it I don't why I said that.
The metal contacts at positions B and C cannot penetrate the card, because the card doesn't have the punched holes at these locations. This is the reason why the springs are needed. The springs at locations B and C compress because the metal contacts (B and C) cannot penetrate the card. Thus no current passes through B and C resistors.
Anyway, you will also need spring guides which will guide the metal contacts in the right direction without allowing springs to warp. (Analogy: a spring in a pen).
When the user, lets go of the lever, the lever shoots back up to starting position because of the spring.(I've assumed that your punch card is made from some cardboard which doesn't rip as easily as normal paper). At this point the user withdraws the card and goes through door and 5 sec later, the door locks.
You can definately make this mechanical punch card "reader" more sophisticated by using punch cards that have a matrix ( say 4 rows and 4 columns of punched and unpunched holes), but that will also somewhat complicate your digital logic.
Tell me if this works!