Radio Dimmer Problem

Recently purchased a used '03 Tahoe and when the headlights automatically turn on, the stock Declo RDS diplay stays at the same intensity as before the headlights turn on. The other bad part about it is that none of the buttons on the radio itself are backlit. It may or may not be related, but the light on the left side temperature control on the AC is also out. Any ideas? Would this be a radio problem, fuse problem, or a wiring problem? Thanks in advance for any help.

Does this happen with the lights on (tail lights and all) or only with the DRL (daytime running lights)? If only with DRL, this is normal. If not, it's more than likely the dimmer line going to the radio is the problem. The A/C control is probably just a burned out bulb.