The problem is your lighting. It's not really a problems it's more a result. ISO is essentially the quality of your picture. If you're in lower light conditions you'll want a lower ISO, I would have suggested 500-600 for indoor light (set your WB to the little lightbulb). I often boost it up to 1600 for a beautiful sunny day, not indoors. The result of a high ISO and too low light conditions is a "grainy" photo. Case in point. Your picture quality is set too high for the environment, it's TOO sharp which creates grain. Try putting your camera in Aperture Mode (A) and put the aperture to say... 5-7. Either auto focus or manual, doesn't matter. I've been using the Nikon D80.
Great cameras, Nikon does make.