ON my previous CX-5 (2013) my key fob battery drained completely. Tried to open the car and it was not working at all so I forced my way in by opening the trunk and then the back door. Replaced the car battery ( initially I wrongfully assumed that the car battery died) and started the engine and I had exactly the same behaviour. It turned out that, in my case, by "breaking" into my car, the anti-theft system kicked in and that's why I had all the symptoms that you've described here ( according with the Mazda mechanic who fixed my car). You might wanna consider this avenue, too.