Why doesn the Range Vent Hood light work?
The first thing that you need to check is the light bulb. If the bulb is blown, replace it with a similar bulb to the one you removed. If the light doesn’t work after the bulb is replaced, but the fan is working, then check the light switch (in the on position) and the light socket for continuity. If one or both of these do not have continuity, then replace the item.