you have not done a thorough analysis or have not communicated all that you did.
For starters, “not turning over” would indicate the engine isn’t moving as opposed to “not starting” which would indicate the engine is trying to start by ”turning over”.
If it is not turning over then you must listen to see if you hear the starter solenoid working and pulling in the gear to the flywheel. If you don’t hear that, then a battery test is in order. If that is good, then you must determine what is wrong with the solenoid == wire, connection, solenoid, or ignition key or circuit.
If it is pulling in and the starter isn’t running, then either, the starter relay which is part of the solenoid/starter assy,, the starter itself or the engine is frozen up. A frozen engine would be indicated by severe dimming of lights when the starter engaged since it draws significant current when locked.
HOWEVER, with the dash indicator you are getting, you may have a coolant sensor that prevents the car from turning over if the water is low or the sensor is bad. You will have to research that.
I would recommend doing a little more analysis and searching for a BMW forum to ask the question.