Welcome. I will try my best to help you and in order to do that, I need you to describe as best you can because I only know as much about your problem as you have told me in your post, so my answer will be based on what you have posted. Please feel free to reply as needed.
If there is one light out, it will not prevent the one remaining light from coming on. IF they both are out then you may have issues with the BCM, headlight switch or dimmer switch provided both headlights are not burnt out.
Chevy Technician
GM Grand Master Technician 2007. 9 years Automotive experience, 7 years with GM. Just Answer Mentor