Two or three second delay before cranking/starting, now, it does not crank?

There are two relays that run the system, one is the inhibitor relay, and the other is controlled from the smart entrance control unit. Either of these can be causing the problem. Here is the location of the relays and the starter wiring diagrams so you can see how the system works. I would make sure the battery was in good shape because I have seen low voltage cause this problem.

https://www.2carpros.com/articles/car-battery-load-test

Check out the images (below). Please let us know what you find. We are interested to see what it is.

Sure, here is the security system wiring diagrams with relays so you can see how the system works. Check out the images (below). Please let us know what happens.