I have progressed in finding the cause of the engine not starting.
I hope it can be useful to someone else.
The cause is that there is a contact issue with the Park position of the transmission.
To start the engine: I pressed on the brakes firmly, I put the transmission to Neutral (to do so, removed the little cap to the right of the transmission arm) and turn the key to start. Voila!!
Now what I need to know is: is it just a little adjustement that is needed and can be done easily by myself, or is it more complex and require a trained mecanics?
(for the rattle, I had a health issue and will deal with it soon).