Some of these vehicles have a switch that turns off the int lights, so the lights don't come on when the door is open......check owner's manual for location....sometimes located in overhead console....
Your headlights come on as soon as you turn key on? Are these DRL's(daytime running lights)? Apply e-brake, then turn key to on....if light's don't come on, it's DRL's....
If you have auto headlights, could have a bad light sensor, or the sensor is covered on the dash......
Easy to tell the difference......if auto lights, the brightness of the radio display would go dim in daylight....if the radio display stays bright, it's DRL's.....DRL's are usually half the brightness of high beams...