Hello, I had the same problem a few days ago with my new P1S in December 2024.
I am answering cause I solved the problem and seems still an issue at P1S.
I located non correct connected pins at the cable. The cable is pinned at the plug and fixed with glue. Nevertheless some pins was pushed out when the cable was connected/pressed by me at the screen board. Therefore the buttons didn’t work.
After inspecting and locating the problem I pushed the pins back into the plug.
Problem solved. Buttons working!
Probably this hint can help somebody. Not necessary to send any part back.