The passenger side air vent on my 2010 XF Jag stopped opening on start-up but would close on shut-down if I opened it by hand. Conclusion the motor still worked and it was not jammed.
This link was the answer for me…
A small plastic component in the vent cracked and this video shows how to replace it. What it does not show is how to take the dash apart to get at the vent. The workshop manual does tell you but its fairly basic. So all the panels you need to remove snap off with one exception. The stainless steel panel snaps off but also has two screws holding it on. They are easy to get at but deeply recessed in the front of the panel. I could not see what was holding it on and eventually pulled it off causing some damage.
This video although solving a different problem shows you how to remove the bits you need to get at the vent. Don’t remove everything they remove, just the bits you need to get at the vent.
It took me two hours because I took my time and $6 for the plastic widget. I also spent another $6 on these…
https://www.amazon.com/dp/B00HNMLQAG?psc=1&ref=ppx_pop_dt_b_asin_title
Well worth the money. Hope this helps.