Alarm and immobiliser problem

Hi everyone pls pls can someone help me. We'd night for no reason and for the first time I've had my 2004 45 the alarm started going off and wouldn't let me turn it of with the fob I had to use the key and turn in the door right then left. The car wouldn't start. I got a jump start alarm started going of again repeated key in the door it stopped. I went to the garage he said the alternator is fine but battery is a little low. So I bought a new battery yesterday an exide one fitted perfect. Then at 01.15 this morning started going of again no hazard lights flashing just alarm. And same again would only turn of with the key in the door and still won't start. Pls pls help. Thank you

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