Transmission cable unhooked it will not shift into reverse or park

Do you mean you can't manually shift to reverse or park with the cable unhooked or with the new cable it doesn't have park or reverse? Check out the diagrams (Below).

If you haven't already, here are the directions for cable adjustment:

When moving the shift lever from P to R with the ignition switch ON and the brake pedal depressed, make sure that the shift lever moves smoothly and correctly into position.

Start the engine and make sure that the vehicle moves forward when moving the shift lever from N to D and moves rearward when moving the shift lever to R. If the operation cannot be performed as specified, inspect the park/neutral position switch assembly and check the shift lever assembly installation condition.
ADJUST SHIFT LEVER POSITION

Apply the parking brake and move the shift lever to N.

Remove the console box assembly. [ INTERIOR PANELS / TRIM: FRONT CONSOLE BOX: REMOVAL ]

Disconnect the end of the transmission control cable assembly from the shift lever assembly.

Using a screwdriver, pull out the stopper of the transmission control cable.

NOTICE:

Do not remove the stopper. If the stopper is removed, reinstall it to its original position.

Rotate the nut counterclockwise approximately 180°, and while holding the nut in place, disconnect the transmission control cable from the shift lever retainer.
NOTICE:

Do not over-rotate the nut as it will come off the internal spring and the transmission control cable will not be reusable.

Push the 2 claws together at the top of the transmission control cable lock piece. While holding the 2 claws together, push the 2 lugs on the bottom of the lock piece toward each other and upward to pull out the lock piece.

Turn the nut of the transmission control cable 180° counterclockwise. While holding the nut in place, push in the stopper until the stopper clicks twice.

Install the outer part of the transmission control cable to the shift lever retainer. Check that the spring is positioned at "A" and push in the stopper.

If the stopper cannot be pushed in, slightly turn the nut clockwise and then push in the stopper again.

Install the cable end to the shift lever assembly.

NOTICE:

Check that the lock piece is pulled up.
Install the cable end all the way to the base of the pin.
Push the lock piece into the adjuster case.

NOTICE:

Securely push in the lock piece until it locks.

After adjusting the shift lever position, check the operation and function of the shift lever. If there is a problem, adjust the position again.
Install the console box assembly. [ INTERIOR PANELS / TRIM: FRONT CONSOLE BOX: INSTALLATION ]

Check out the diagrams (Below). Please let us know what happens.

Hi,

As far as the park neutral switch, is that where the shifter linkage is attached? Are you sure the shaft going into the transmission is moving when you turn the shift lever to park or neutral?

I call that switch a range sensor. I can't remember on this vehicle if it is electronically controlling shift or not. In the vehicle, is the gear indicator a light?

Joe