Assume your dash lights dont dim or go out when you turn the key or you would have said so. First thing to check is if you are getting a voltage at the small solenoid terminal when you turn the key. If not you need to work back to the key via the starter relay and possibly immobiliser. As its an auto there will be a switch to stop you starting it in anything but P or N. Worth j-j-jiggling it about a bit as Arkwright would say.