if the battery is flat you can crawl underneath and put jump leads on the starter cables/connections, possy on starter and neg on body/engine/earth point and jump it from another car, this should allow you to put your eka code into the drivers door and then sync the key, the door lock mech bieng faulty presents a problem!!!
you can strip the door lock mech down and free it off and regrease it and put it back, you have nothing to loose if it doest repair then you can always get a new one!!