I would start by checking your headlamp switch, as this is also your dimmer switch for the dash lights. You will most likely find that the connector has melted inside the switch or has a burned contact. To get at the switch you need to pop off the side panel on the dash, & partially remove the front dash panel that surrounds the instrument panel. The switch is held in place by 2 7mm screws. If this is not the problem then your instrument cluster panel is bad. Hope this helps.
Source: GM Certified Technician