After reading many stories online and finding out that my doorbell is about 4–5 years old, I was quite sure it was dead as a door nail.
There was no lights, nothing.
The only thing which indicated that it had any life left was that it was intermittently connecting to the WiFi in this state.
I had almost decided to replace it before I tried one last thing.
I opened the face plate with the screw driver which came with the box (the screw is under it).