The D80 can give grainy results in shadow areas even at ISO 200 in bright light if you look in detail at the images pixel by pixel. I have a D200 that gives this same result. You should not see significant graininess in normal ISO 200 images in lighter, uniform areas of the image like the sky or a light-colored blank wall.
It's also possible that you are shooting at higher ISO if you have Auto ISO turned on, even if your normal ISO setting is 200. You need to use the menus to turn off Auto ISO, or set it so the highest ISO it chooses on Auto ISO is 400. If you're using Aperture mode with a small aperture or Shutter mode with a fast shutter speed, you could wind up with a high ISO setting from Auto ISO when you don't expect it.
If you check the Shooting Data in Picture Project when you import, or the File Info in Photoshop or Photoshop Elements, it should give you the actual ISO the camera was using when it took the picture, and tell you the aperture and shutter speed.
Underexposure is another potential reason for noise in the image. If your images look dark, that's a sign that underexposure is an issue, and you can use the exposure +/- control to adjust it.
Other sources of things that might look like grain are JPEG image artifacts if you are using Normal or Basic JPEG settings. These artifacts will show up most prominently as a scattering of darker pixels around dark objects with relatively uniform light backgrounds, but should not extend far into uniformly bright areas of the image.
If your "grain" is circular spots slightly darker than the background that are larger than a few pixels and show up on all the pictures in the same place, you could have dust on your sensor, which requires cleaning with a blower or special sensor cleaning kit with the shutter open.
If none of these things turn out to be the source, it's possible that something has gone wrong with the processor board, sensor or sensor amplifiers, though I would consider this unlikely. Those would require a processor board or sensor replacement, which may not be worth the cost considering the cost of replacing your camera.