Since it doesn't go into park, the first thing I would check is the shift linkage to make sure everything is attached and properly moving.
Here are directions specific to your vehicle for adjusting the shift cable. If this isn't the cause and it still doesn't hold in park, I suspect there is a broken CV joint causing the issue.
2005 Buick Truck Rendezvous AWD V6-3.4L VIN E
Vehicle Transmission and Drivetrain Automatic Transmission/Transaxle Shift Linkage Shift Cable Adjustments
Automatic Transmission Range Selector Cable Adjustment
Notice: Adjust the automatic transaxle range selector cable while the transaxle and while the gear selector are in the Neutral position only. Failure to do so may cause mis-adjustment.
1. Set the parking brake.
2. Block the wheels.
3. Use an appropriate tool to pry on the automatic transaxle range selector cable terminal at the automatic transaxle range selector lever pin to remove the automatic transaxle range selector cable terminal from the transaxle manual shaft lever pin. DO NOT pry and DO NOT pull up on any other part of the automatic transaxle range selector cable or damage may occur.
4. Fully lift the adjuster lock button. Ensure the adjuster is free to move.
5. Rotate the automatic transaxle range selector lever fully counterclockwise to the Park gear, then rotate the lever clockwise 2 clicks into the Neutral gear to place the automatic transaxle range selector lever in the Neutral gear.
6. Perform the following steps to place the inside car gear shifter in the Neutral position:
1. Rotate the shift lever to the Low 1 position, fully down.
2. Push forward on the lever while slowly pushing up. The gear shift lever moves up while clicking over the gear over travel stops.
3. Release the gear shift lever once the gear shift lever stops solidly. The gear shift lever is in the Neutral gear.
7. Grasp the automatic transaxle range selector cable terminal in the underhood.
8. Pull the automatic transaxle range selector cable terminal toward the pin on the automatic transaxle range selector lever. The automatic transaxle range selector cable adjuster spring should compress as the terminal is moved toward the pin.
9. Carefully push down the pin until the pin snaps to attach the pin to the automatic transaxle range selector lever. Do NOT move the automatic transaxle range selector lever out of position. DO NOT pull the terminal beyond the pin then push back or the shifter may move out of the Neutral gear.
10. Press the adjuster lock button down flush with the adjuster body.
11. Shift to Park.
12. Release the parking brake while applying the service brake.
13. Start the engine.
14. Ensure all the indicated gear positions match the vehicle response.
The third pic shows the cable where it attaches to the transmission range sensor. Do me a favor. Pay attention if the gear shift indicator in the vehicle is accurate. For example, does it show P when you are in park.
Let me know.
Images (Click to enlarge)
Saturday, January 18th, 2020 AT 9:38 PM