Is Long Exposure Noise Reduction turned ON? After you capture the image do you see Job nr blinking in the viewfinder?
You are obviously shooting in very low light. Given the slow shutter speed I would expect the images to be blurry if you are not using a tripod.
Does the built in Speedlight pop up when you are in Auto mode?
Try setting the camera in Manual exposure mode with the shutter speed set at 1/60th sec. or faster. Is the camera ready to capture another image immediately or is there still a delay. (Note: the image will probably be very dark.
What happens in P, S, A, or M exposure modes when you shoot outdoors in daylight? Good Luck and Enjoy your Nikons!