Manual shooting mode problem.

The exposure compensation dial (at the back) doesn't work when you're in Manual. In Manual, you set the shutter speed and aperture to get an image with the amount of over- or under-exposure you need. In the view finder, the "exposure meter" at the bottom shows how much light there is where the lens is pointed. When it shows what you called "2-stops", its really underexposed. Thus your black images. You need to increase ISO, open the aperture and slow down the shutter speed (or a combination of these 3 options)

Set your camera to P or full-auto. Do the photos turn out ok? If they do, then there's nothing wrong with your camera and you just need practise on the Manual mode.