904 pushbutton with no neutral

Hi all,

This problem has ben getting progressively worse on my 64 Valiant. I depress the Neutral button (and in return it depresses me) with no effect. it stays in drive. It shifts through the gears and reverse normally. I've had the transmission serviced without effect. When I use the parking lever, that works fine. One final piece of the puzzle is that it has always had trouble starting in Park. And I have had to go though the routine of having to find the sweet spot with the buttons before she'll fire.

I looked in my 64 Chilton's and it kind of says start over, pull the cable. But before I did something that could potentially sideline my car I was hoping for a little advice.

Thanks!