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If I'm not mistaken, I believe there's a cable that goes from the shift lever to the trans itself. They have a tendency to bind up and end up snapping.
You have a problem with the shift interlock system. When you step on the brake pedal, the brake switch energizes a solenoid on the steering column (steering column shifter) or console (floor mount shifter). That moves a pin out of the way so you can shift.
The problem can be a fuse--check fuse #28
or a bad Brake Pedal Position BPP switch
or a bad solenoid
or a bad shift interlock cable.