How to start my 2009 elantra to a new transponder key?

Question edited for clarity and English.

Reset the anti-theft system because you disconnected the battery.

https://www.google.com/search?q=2009+suzuki+xl7+reset+security+system

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The short answer is you can't!

The coded transponder is needed to disarm the immobiliser. There is no quick, easy or cheap method to overcome the problem. If the spare key doesn't work either you will need the dealer or an auto locksmith.

This type of work normally requires diagnostic or key coding equipment .

You will have to take the vehicle to a Mazda agent and ask them to program a transponder key for your car. Every key is specially programmed for a particular vehicle according to its VIN number.

The dealer will ned to use the diagnostic scanner to program just one fob. If you you have two good ones then you can do a third or fourth.

Remote can be matched manually

Have you tried a new battery? If you di and the issue remains the remote is likely defetive.

when the alarm is going off, use the key to lock and then unlock the front passenger door lock.

This means that the programming of the Transponder Key has been corrupted or the Programming data of the Key in ECU ( Electric Control Unit ) has been lost or not responding. You now have to get a new Transponder Key. You can get it on E-bay for $30. After you receive it, reprogram the car to the New Transponder Key to the ECU ( the process in usually given in the instruction manual or in the Service Manual ). Then the car will start perfectly.

You can take a new transponder key(s) (dealer issue for current lockset) and remote(s) (ebay) to the dealer for a complete reprogram. Whomever stole your original will still be able to get in your car, but will not defeat the alarm system nor be able to start the car. The alternative is to replace the locksets as well and nobody has the cash for that.