I don't think you have the lens you say you have. You seem to have a lens with an aperture ring, which no G lens does. I think what you're referring to as the "small metal adjustment nub on the backside of the lens" is actually the aperture ring. Do you perhaps have an AF-S 28-70mm f/2.8D?

When using a lens with an aperture ring on your D750, you need to set the ring to the minimum aperture for that lens (f/22 in this case) and control aperture using one of the command dials. If you do not set the aperture ring to f/22, the camera will be unable to stop the lens down to f/22. In fact, by default it will refuse to take a picture when the ring is not set to f/22. (There is a way to change this behavior and use the aperture ring to adjust aperture, but that option is buried deep in the menus and is probably not relevant to your issue.)

You say the DoF Preview button does not change the apparent light level in the viewfinder—but it must, unless either it's broken or the lens's aperture lever is broken. You said your other lenses work fine, so I assume the camera's aperture control unit is fine.

Tell me this: when you turn the aperture ring—without holding down the DoF Preview button—does the image in the viewfinder change brightness? It shouldn't; the brightness should stay the same. If it does change, it means that the aperture control arm in the camera is not mating correctly with the aperture lever in the lens bayonet. It may be that the aperture lever is bent so that it's not making contact with the control arm. You can try gently bending it straight. Look at your other lenses to see how the lever should be.