Highlights are not very white and shadows are not very black. Slides have at several times the contrast range of a print. That's because they work by blocking the transmission of light. If the slide is very clear, the light source comes through almost undimmed. In portions of the slide that are nearly black, the light source is obscured.
Computer monitors are closer to slides than prints in their ability to represent contrast.
Shadows correspond to portions of the monitor where the phosphors are turned off. Consequently, any light that comes from these areas is just room light reflected off the glass face of the monitor. In a dimly lit room, it is easy to get a 256 to 1 contrast ratio. You'll start by slapping a photo down on a flatbed scanner and then you'll never get the full range of tones that was present in the original negative or slide. But if you use PhotoCD or some other form of negative or slide scanner then you have a chance of achieving Web greatness.