No, dome light is not controlled by the dash rheostat dimmer switch.
Also, do you get the door chime when the keys are in the ignition? If not, then that's a sure sign that the door jamb switch is stuck or not working. Which explains why your dome light doesn't come on. They're both controlled by the same switch in the door jamb.
And, I'm not trying to be a smart-ass when I ask this - but have you tried replacing the bulb for the dome light? They burn out pretty regularly.
Above your rear view mirror between the sun visors, you've got your courtesy dome assembly. Middle switch controls middle light which is activated when you open either passenger or driver door. There is a slide switch in the middle. It should have, as Spiffy stated, three positions, on - door - off. Make sure its in the 'door' position. You also have two map lights on either side of that dome light assembly. Push the buttons in to turn them on. Again to turn off.
Your car also has courtesy door lights so that the ground is illuminated when the doors are opened, and to help other people from ripping your door off when they drive by at night. These lights in the very bottom, rear corners of driver and passenger door should illuminate any time the door is open.
All of these lights mentioned are controlled by individual switches in driver and passenger door jamb. On your car it's a small, squarish housing with a round button, sealed in rubber. It's below the door striker. (what the door latches onto)
Start by checking the switch setting. If the light doesn't come on in the "ON" setting, your bulb is most likely blown. In the ON position, the light lights and stays on whether the doors are open or closed. This is the easiest test. No light in ON = BLOWN BULB.
If it comes on in the "ON" setting but not in the "DOOR" setting with the doors open, then your switch is probably stuck. The dome light is independent of each door switch. So it might work when the passenger door is open, but not when the driver door is open and vice versa. Test and see.
Move the dome switch to DOOR. Open the driver door. If the light doesn't come on, use your fingers and push in on the door jamb switch (for the door you have open) bang on it, tap it, etc. If the light still doesn't come on in the DOOR setting, but does come on in the "ON" setting, then you've got a bad door switch. Repeat for the passenger side. Make sure you only test one door at a time with the other door closed or you won't know which switch is or might be bad.
I've highlighted the switch location in the green box in the picture. This is a 2000 Prelude driver side image. Switch is identical in placement on the passenger side.

- DOME LIGHT DOOR JAMB SWITCH
Replacing the bulbs in the dome and door panels, is very simple.
Pictures to help locate lights, switches and how to replace.

- ALL Light and Switch locations

- Dome Light Switches and Bulb Replacement
- Image3.JPG (8.87 KiB) Viewed 14909 times

- Door panel courtesy and bulb replacement
- Image4.jpg (11.09 KiB) Viewed 14909 times