Check to see if the dimmer/illumination circuit on the radio is connected or not. There are different types of dimmer/illum circuits, and often there are more than one type of dimmer/illum inputs on aftermarket radios to be compatible with the common ones.. If the wrong one is connected, that can cause lighting problems sometimes.

Other than that I would just say it's probably a fuse problem. There is usually more than one bulb on the climate control unit, so if you have no lights at all then I would look at the illumination power, not the bulbs.