Did you buy the D4 from a local dealer? Mine would trade me for another one right over the counter with the only paper work being serial numbers.
The one I shot was perfect from the start. I would have kept it if I could find the money.
First test: I changed to best quality, Large, and Fine JPEGs. I can't remember anything else except maybe Aperture Priority. Then I machine gunned down a line of camera students waiting for their teacher and took a few random shots around the shop. When I got home and zoomed in on my Computer Monitor, every one was in sharp focus.
I would trade or send it in. I've only gotten one lemon from Nikon in 12 years and dozens of products, but they do happen to all Manufactures.