Cranks but wont start?

Those are not interchangeable, they are programmed to each cars VIN and options coding. Just swapping one in that is incorrect can kill it.

The easiest way to be sure is to put a scan tool on it and query the module. BUT if it is the immobilizer you will be visiting the dealer to get the coding to program a replacement to make it work. No way around that now as the companies are getting real tight on the security systems.

P0113 intake air temp sensor circuit high - Check the wiring from the IAT to see if it is broken. The picture shows the sensor. It's a simple heat detecting resistor. They do fail but the wiring is the more common issue.

Yes, the key, ECU, immobilizer are all VIN linked. Basically most of the security systems in vehicles work the same way these days. Setting still the system shuts off the injectors or starter or both. When you get in and put the key in the ignition or get close to the car with the electronic key, the security system reads information from the key/ignition switch/transponder. Then it tells the ECM/PCM/ECU if the device is the correct one for the vehicle and that it can start the engine.
To make sure that stealing the vehicle isn't as easy as simply plugging in a different used module from a similar model, they also use the VIN or other security code to verify the components of the security system. They also code that number into other modules on the vehicle as well to make those useless if stolen.

For instance on many newer vehicles the dash, BCM, radio, ECM, ABS, Fuel pump control, and other modules, are all part of the system and are all coded against not only theft but even simple removal. Remove the factory radio from many cars these days and you lose the door and warning chimes, the memory seats/pedals/mirrors and on some the security system will shut the car down.
Want to swap out your base model instrument cluster for the super deluxe version? You need a dealer level scan tool and the factory coding to make it work.