Ooookay, now I found a solution. When I tried charging via USB from the PC, the phone came back to life. Some would think that this means that the AC charger is broken, but after coming back to life the AC charger can continue the charging proces.
Reason I even tried the USB approach? I suddenly had the exact same problem with my 950XL that I had in my drawer (out of battery).
Cheers
Rene