Cycle selection buttons and timer knob stop....
Patrick -
You are on track about the cycle selector buttons and timer. The user is supposed to depress a cycle option button, then that button determines which cycle of the three or four in the timer is used. The water temperature that goes along with is determined at this time as well by the timer. When the cycle button is pushed, a mechanical pin is set to engage a slot in the timer, and lock the timer from rotating (this is where the stop comes from) until the knob is pushed in to start the machine. This way if you know you are washing white cottons, you just push that button and turn the knob until it stops, then push it in and go - the machine is supposed to run the white cottons cycle.
One simple suggestion would be to press a couple of the major cycle buttons, white cottons then colored wash and wear, etc, and make sure the pin selector system is not in "neutral". On the couple machines I have, you can lightly depress a button and make it release the old selection but it won't select a new one. At that point the timer just "free wheels" until a cycle is firmly selected.
I have seen them when the pin stops no longer work as well. I have a machine just like yours in my storage (in white) so if you can't make that function work, maybe I can access mine and with pictures etc. we can determine what is not working on yours.
Let me know if I can help you - there are a number of knowledgeable people here so I'm fairly sure that someone here will be able to help you get over any hurdles you have.