Well I just corrected the same problem here yesterday.
When I didn't see a fuse or even relay under the hood, I asked the previous owner (who is a retired auto/heavy duty mechanic.)
He suggested disconnecting the battery. I did for approx. 30 minutes and the problem rest itself!
I only had to reset the clock as all of my radio preset remained intact.
Hope this helps.
(Also NOTE: When the dash lights are working and the dimmer control is turned completely to the down position, the dash lights are still visible - very dim.)