care will not start

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When I try to start the vehicle, it will not start. The battery is new, powerful still. All lights go on. Does not "turn over". Everything else is a go, including lights. Car won't turn over, start. I have tried leaving the car. Using the alarm button outside. the key in all doors and the trunk. There is one door handle that is fell out. I still have the entire mechanism. It needs to be put back in the door. I don't know what happened but the last time I got it back from the mechanic, my car was fine, and then when I went to access the back left passenger door handle, it came out in my hand, fully intact. Thank you.