New ECM installed and it will not start?

I'm sorry to say that this is a common problem with "preprogrammed" parts. They don't have the exact keys you have in the shop so they cannot program them in. As such you end up with the PATS system shutting down the vehicle. As for the keys being recognized in the doors, that is because they are read by the body module. The ECU on the other hand gets the key information from the BCM and compares it to its internal memory of "legal" keys and if it matches it will let you start the engine. If it doesn't you end up in your situation.
You can try the 30 minutes relearn procedure but unless they set the ECM up to allow it you will likely need either a locksmith or a dealer to go into the PATS module, erase any current keys and then enter in the ones you have. Then see if the replacement ECM fixed the problem.
30 minute relearn -
A total of eight keys may be learned to a single vehicle.

This procedure will only learn the vehicle key information.
This procedure will not learn any immobilizer information between the body control module (BCM) and engine control module (ECM).
If the battery voltage is low, charge the battery before continuing with the procedure.

With an unlearned master vehicle key, turn ON the ignition, with the engine OFF.

Observe the security indicator, after approximately 10 min the indicator will turn off.
Turn OFF the ignition and wait 5 s.

Repeat steps 1 - 3 two more times for a total of 3 cycles or 30 min.

The body control module learns the key transponder information upon the next ignition transition from OFF to ON.
As such after you complete the third cycle you need to turn the key off. Now try to start the engine, if it works you will have a running engine.

Start the vehicle. The vehicle has now learned the key transponder information.

To add the remaining keys you start with the key you just programmed in.
Turn that key on and verify the security light goes out. Turn the key off. Remove that key and insert the next key and turn the ignition on within 10 seconds. Repeat for the rest of the keys.

If the above doesn't work you will need to use the scan tool to do the programming.

It might but using a scan tool is a lot faster and easier really. It depends on how they set up the ECM before shipping it.