The tailgate only opens partially, about 1 foot then beeps a couple of times and won't go further.

Question edited for clarity, name of maker and spelling of 'Cayenne'.
Question moved to category.

Seems to be a known issue.

https://www.google.com/search?q=2011+porsche+cayenne+tailgate+won%27t+close

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Procedure for 2002 Land Rover models:
1. With the doors shut and from inside the vehicle.
2. Turn ignition to position 1 and back to off within 5 seconds
3. Remove key from ignition and press and hold the unlock button (has
an arrow on it) for 15 seconds during this time press the key lock button
(has Land Rover logo)3 times within 5 seconds
4. Release both buttons
5. Doors will lock and unlock to show correct programming has occurred hope this helps

try using a scanner to reset the CPU program in the ECM as it may be corrupted from the battery change

CHECK THE FUSES

This video should solve it. If the window is not dropping enough see the video at about time 4:10 where a problem causing this can be seen followed by a solution. https://youtu.be/xLQOzLaq5mw

Check your fuses under hood above battery opens right to left

there are bolts on the side of it and on the back and posiblly the bottom. take them out. just watch when you take out the ones in the middle of the back side your handel will fall out. take off that black cover.and you should be able to see inside of the tail gate.

Try to reset the tailgate by removing the no.7 (7.5 amp) fuse in the underdash fuse box. Open and close the tailgate manually, reinstall the fuse, and try the open tailgate button. If that doesn't work you would have take it to the dealer, where they can check for DTC's (diagnostic trouble codes). Honda Al

it sounds like the window regulator