There is absolutely no module by itself in the car that if it was going bad would engage the starter, pass a matching security code to the ECU, and have the engine run.

No Crossfire engine will run without the KEY-SKREEM-ECU communications!

The more recent exception, that does not apply in this situation, is an ECU modified by a third party like Precision ECU to eliminate the SKREEM. Even then there is no module that would both engage the starter and turn on the ignition power so the engine would run.