1989 Buick Century dash light

If all the dash lights (back lighting to read gauges) are out then it is more likely the switch where you turn your lights on and the dimmer controll to dim down the dash lights.

Silly question, maybe, but is the dash light dimmer simply turned down too low?

If only one bulb is burned out by your speedometer and other backlighting dash lights work it would be a pretty big job to replace one small bulb. You have to take the dash apart including removing the instrument panel. Lights like brights, turn indicators, etc are seperate from the rest of the dash lights.