I have a '93 Accord and had what sounds like the same problem. If your tailights still work and it is just the dash lights (excluding the clock and radio) it is most likely your dimmer switch for the dash lights. If it is at least a '90-'93 (not positive for other years/models), you can remove the dimmer from the dash and disconnect it. Then ground out the red lead to ground. If the lights come on, it is your dimmer that is bad.