Hi,
This is an odd one. I don't want to, but I have to ask if you tried a different FOB or confirmed the one you are using is good. As I believe you are already aware, the P0513 deals with an invalid skim key. This is causing the immobilizer to engage. This could be an issue with the body control module, the RF hub module, PCM, and so on.
Since this happened when replacing the battery, check all fuses if you haven't already to make sure none have failed.
Also, if you are unable to delete the code, there is a chance something is interfering with the RF interface or something was damaged if an actual theft attempt was made.
As far as the codes are concerned, it is based on the type of scanner you are using. If you have a scanner that can scan the can-bus, that will provide a lot more info. Because this is a 2016, that is what you should be using. Take a look through this link and let me know if this is what was done.
https://www.2carpros.com/articles/can-scan-controller-area-network-easy
I am going to provide the diagnostics for this code. See if anything helps.
Let me know.
Joe
See pics below.
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Saturday, May 14th, 2022 AT 9:04 PM