With the cable shift transmissions you have two cables, one for shifting from neutral, drive, 2nd & 1st and one cable for park. the shift cable could be broken or unhooked inside the trans but your park cable could be working fine. So the car shifts out of park but isn't shifting to any gears.
First thing is make sure the fluid is correct level. Then check the shift cable. All the pics below are from the 65 service manual.
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Because the shift cable is attached inside the transmission at one end and the steering column at the other sometimes it is bard to tell is the shift cable is moving anything. If you move the shift lever from 1st to 2nd to drive does it feel really loose or does it feel like it is moving something?
This pic shows cable attached at the steering column and at the transmission. Lok at the adjustment section below to see how to verify the cable is connected, moving correctly and adjusted.
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