The Wire ! It was it, the white one connected to the input pin. I should have thinked to test it when you suggested to test the button. It's so simple to check with the ohm meter...
My first failed wire. Another thing learnt by experience! Note for the future: CTFW (check the f****** wires).
Thanks @ReverseEMF for the solution and all the others for your time.
Gaël