Bring the power directly from the battery to fuse 52, please. If the car starts from this you will know that it is a relay problem/SAM contact problem.
When you do this, yes the gear shift will be locked in park; yes, you can release it manually and yes, it will lock again when it is put into park.
I have encountered this problem on a number of occasions. I have always carried out this procedure or advised another to carry out the procedure and it has always been a relay and /or SAM contact problem.
I am not saying for sure that this is your problem as I do not have your car in front of me, but it is the simple test and the cheapest test and it is what you should eliminate or discover in the first instance.
If the car starts in this manner there will be little doubt that it is a problem as I have outlined and then we can take it from there.
When I first encountered a similar problem if I listened to all the forum suggestions-well intended- I would have had a new battery, or a new switch, or a new selector, or a new SAM and even a new ECU.
it has always been a relay/SAM connection problem in my cars X 2 and in the other cars that I have had an input into. So keep it simple in the beginning.