Yes. Mine did this right out of the box at the camera store - in the hands of a service tech the day they first received some D600's.
It has done this 3 times since. A 2 button reset allowed it to work, the 2nd time. But the first time it went JUST like your experience, and we had to remove the battery. 3rd time it allowed me to turn power off and on again with renewed proper function.
Seems related to accidentally pushing the zoom and "joystick" at the same time.
I am promised a trade out if I want to keep it, and have feared getting a dust/oil issue which I DO NOT HAVE on this body.
LOVE to hear from the gurus whether to trade or keep what I have. Of course I also have a warranty.
Local shop says they have NOT HEARD OF THIS ON ANOTHER body. Well, now I have. I am concerned for both of us. Are there others?????