What I'm asking is:
Will the motor start in the neutral positon? (it should)
Does park hold the vehicle from moving like it should?
Try this: Before putting the shifter in park, set the emergency brake firmly. Then put it in park.
If my theory is correct, the parking brake will prevent the park pawl from engaging (the slight click you normally hear after the car rolls a few inches before park engages and holds it) and that lack of additional bind on the cable may allow you to move it out of park and into gear engagement without rocking the car. If so, the cable is fragged. If not, I'm stumped.
If this gets you nowhere, I would disconnect the shift cable from the selector lever on the tranny, and see if each range can be selected with the cable out of the picture by moving the selector lever....especially to see if reverse can be selected...