This sounds more like a hardware fault than a setting issue. Based on the community responses, the best next step is to have Nikon inspect it and provide a repair estimate.

The Nikon 1 10-30mm lens did have a known common fault, often causing a black image, and Nikon repaired many of those lenses. However, your symptom—camera shutting down in most modes except Smart Photo Selector—doesn’t match that typical lens problem, so it may be a different camera or lens fault.

If you haven’t already, you could briefly test with another compatible lens or check whether removing/reseating the lens changes anything, but the advice given points to professional service rather than a simple user fix.