After replacing the battery, the engine cranks but does not start

Just some basic checks first. It does sound like this is a theft issue so here is a guide that will help with deactivating the system:

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

Next do you have a proper transponder key? Basically, this sound could be a key with a chip in it that will allow the vehicle to start.

If this is a new vehicle to you then there is a chance that the previous owner bypassed this system and by disconnecting the battery, it caused it to reset.

If this is not the case, then we need to scan for codes.

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

If there are no codes, then I am attaching some info that will help with this.

Let's run through this info and let me know what questions you have. Thanks