My battery recently gave out and after replacing it the vehicle goes into accessory mode by itself and the alarm randomly goes off. I can only stop the alarm by putting the key in the door and unlocking it. I’ve attached a video of it turning itself on. Not sure how to diagnose what exactly the problem is.

 

Something cheap and easy to try - disconnect the battery and hold the battery cable ends together for ten or more minutes and then reconnect the battery. On some cars this allows the computers to come back to a base state that can correct some weird function issues.