Your car doesn't have a headlight chime so that has nothing to do with it. It sounds like the wiring that would normally use the key to complete the circuit and enable the door chime has been bypassed or the part of the ignition that is depressed when the key is inserted is stuck in the "key is in" position. I honestly don't have a working knowledge of these parts but, based on your problems, this is my 'best guess'.

hih