Hi fpino,
If the door alarm don't work, how can it go off when you open the door manually?
Do you mean to say you can lock using the remote but is not able to unlock with it?
If yes, it could be something wrong with the transmitter.
Leaving the boot open could have drained the battery, can you start the car now?
I need to know the model of your car, DX, EX, GX etc.