Welcome to 2CarPros.
My first suspect is the transmission range sensor. That is what determine the gear you are in and what you see on the dash. However, you really should scan the computer with a live data scanner to determine if it is faulty. I realize you don't have one, but because of the work required to replace the sensor, it would be with having done.
If you decide you just want to try replacing the sensor, here are the directions. It isn't an easy job. You will have to remove the transmission pan and the valve body in the transmission to access the part.
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The attached pictures correlate with these directions.
PROCEDURES
NOTE: The transmission range sensor is located within the transaxle. To remove the TRS the transaxle oil pan and valve body must be removed.
REMOVAL
1. Disconnect battery negative cable.
2. Remove engine air cleaner and tube.
See Picture 1
3. Remove gearshift cable.
4. Remove manual valve lever.
5. Disconnect transmission range sensor connector.
6. Hoist vehicle.
7. Carefully remove transaxle oil pan and drain fluid.
8. Remove transaxle oil filter. Let transaxle oil drain fully.
9. Remove valve body retaining bolts.
10. Extract park rod from guide bracket and remove valve body from transaxle.
See Picture 2
11. Place valve body on workbench.
See Picture 3
12. Remove TRS retaining screw.
See Picture 4
13. Remove manual shaft seal.
See Picture 5
14. Slide Transmission Range Sensor up the manual shaft and remove.
INSTALLATION
For installation, reverse removal procedure. Tighten TRS retaining screw to 5 Nm (45 inch lbs.). Reseal transaxle oil pan using RTV.
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Let me know what you find if you have it scanned. Also, if I can be of more help, let me know. However, this is my first suspect.
Take care,
Joe
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Saturday, March 30th, 2019 AT 8:18 PM