Just changed battery in 2003 hundai elantra. alarm goes on when key turned. car won't start. alarm remote fob won't unlock doors

To arm content theft alarm.
1. Open the door.
2. Lock the door with the power door lock switch or
the remote keyless entry transmitter. The
SECURITY light should flash.
3. Close all doors. The SECURITY light should go off
after approximately 30 seconds. The alarm is not
armed until the SECURITY light goes off.

If a locked door is opened without the key or the remote keyless entry transmitter, the alarm will go off. The headlamps and parking lamps will flash for two minutes, and the horn will sound for 30 seconds, then will turn off to save the battery power.

you can have a shop reprogram the reciever in the car to accept the remote. once the battery is removed from the remote it resets the code it transmit (Rolling code)

Well when you replaced the battery did anything else on the key fob work? Often times you have to reprogram the remote in order for it to function properly. Try getting inside the vehicle and manually lock all doors with the driver's side switch. Put the master key in the ignition switch and turn the switch to the run position but do not start it. Now push and hold the lock and unlock buttons at the same time until the locks make noise....may take 10 to 30 seconds. After you have the key fob programmed, see if the alarm will turn off with the remote. Did it work? The only way to totally turn off the alarm is with a GM Tech @ or 3 scan tool and go into body control bidirectional controlling procedures or with a very good aftermarket scanner with good bi-directional functionality.
The alarm works via the body control module on this vehicle and i am thinking it uses the PK2 system and if you do not have a properly coded key or the BCM is loosing memory, then check for any and every blown fuse and replace as needed.to start with.. If the vehicle stays running after starting then the bcm/key is reading correctly.

try changing battery in the remote

your setting off the alarm when you open the doors, make sure you turn off the alarm with your remote

Usually when you change a Fob battery you have to re-sync it to the car. Some cars have you lock and unlock the drivers door with the key.
Should be in your owner's manual.

If the passkey is messed up, there will be a light on the dash that says security, or have a picture of a car with a lock thru it. If there is no light when the key is turned forward, then its NOT a passkey problem.

There is NO kill switch on the 2000 Elantra... HOWEVER, there is a thing called the Key Fob (keyless remote entry system). There is, however, a system in place called the 'starter kill' circuit and it is activated when the burglar alarm goes off.... it's called the burglar alarm relay and it is activated to prevent the engine starter system from being used. There are three ways to get the engine started in such a circumstance... 1. use the key fob to 'disarm' the system... 2. put the key in the ignition and turn it to the 'RUN" position and wait until the alarm stops (horn stops beeping and the parking lights stop flashing), then the engine will start.... 3. pull the starter relay from the UnderHood junction box and bypass the starter circuit (key in ignition and in the 'RUN' position), jumper the starter solenoid circuit to energize the solenoid to start cranking the engine -- it should start then.

Do you have a key fob? Unlock the car with that and you should be OK. My sons Elantra is the same way, you can only get in with the fob. I guess the car thinks it's being stolen otherwise. If you don't have a fob, I'm no help