Buick century 2004 headlights wont turn on

I found this. It seems a bad headlight driver module are common on GM.

The headlamp driver module (HDM) is an electronic module that provides electrical power to the vehicle low beam headlamps. The HDM is controlled by a pulse width modulated (PWM) ground signal from the body control module (BCM). The BCM determines the desired lamp intensity using the ambient light sensor, multifunction switch and the park brake switch as inputs. In general, the HDM will operate in 1 of 3 modes:
• Reduced Intensity Mode: This mode is used by features that do not require or allow maximum low beam headlamp intensity such as daytime running lights (DRL) (nominal: 85% duty cycle).
• Full Intensity Mode: This mode is used by features that require full low beam headlamp intensity such as low beam headlamp operation in manual or auto modes (nominal: 100% duty cycle).
• Off Mode: This is the default mode of the system that will occur when none of the features described above are active. The BCM will deactivate its PWM output (0% duty cycle) during this mode.

You probably need a new headlamp driver module (HDM), common problem on GM vehicles.

hooking up a scan tool an checking for codes in the BCM would be the first thing to check

DTC B3802
Circuit Description
The body control module (BCM) monitors the park lamp switch signal circuit and the headlamp switch headlamps on signal circuit in order to determine when the park lamps and headlamps should be illuminated. When the headlamp switch is turned to PARK, the BCM senses that the park lamp switch signal circuit is grounded and the headlamps switch headlamps on signal circuit is open. The BCM will then energize the park lamp relay illuminating the park lamps. When the headlamp switch is turned to HEAD, the BCM senses that the park lamp switch signal circuit and the headlamp switch headlamps on signal circuit are grounded. The BCM will then energize the park lamp relay and headlamp driver module (HDM) illuminating the park lamps and headlamps.

DTC B2575

Circuit Description
When the BCM receives a ground signal from the headlamp switch requesting the low beam headlamps, the BCM will energize the HDM low beam relay by grounding the low beam relay control circuit.