Will not start after car broken into

Yes. Most likely the theft system is active. Do you have any damage to the ignition switch or the door lock switch?

If so, we need to repair that and scan for codes because usually there is a code that will tell us what the issue is.

https://www.2carpros.com/articles/how-to-reset-a-security-system

https://www.2carpros.com/articles/checking-a-service-engine-soon-or-check-engine-light-on-or-flashing

Let us know what codes are there and we can go from there. Also, if the theft light remains on or flashes, try leaving the ignition switch in the on position for 10 minutes. Normally this will allow the system to reset. However, it doesn't appear you have a chip in your key. If that is the case, this may not work but this is not clear from the manual.

Thanks.