Car seems to be dead again - remote will not work

Does this model have separate key for door? Any tricks to get in trunk when you cannot get in the vehicle and remote key chain does not work?

My battery was dead yesterday. Called road service - they got the door open, gave a boost - brought car to mechanic who sold me a new battery. Came home, parked car - used remote to lock and alarm vehicle.

Wake up today - car seems to be dead again - remote will not work - cannot get into vehicle again! The key I have for ignition does not work in the door. It's the only key I was given at time of purchase.