This problem is more than likely the headlight door relay module, the relay is located in the top center of the dash where a speaker would be.
If the headlights do not come on as well as the door don't open then the problem may be the headlight switch, it controls the headlights and the ground side of the relay closing coil. The relay should be fairly cheap. The headlight switch is very cheap as well, to replace it you reach behind the switch and press the silver button at the rear top of the switch, at the same time pull the knob out, once the knob and shaft are out just remove the male threaded nut that secures the switch to the dash panel. Also make sure you like for heat damage to the wires in the connector to the switch, all the terminals should be bright metal, if they are discolored the connector must be replaced with a repair connector. See picture of switch below.
STANDARD MOTOR PRODUCTS Part # DS273T [headlight switch] $11.28