how is the engine fan going to run if the car won't start?
Because the two are not related - the engine starting has nothing to do with fan operation, fan operation is electronic.
When you turn the key to "ON", the Fan Module powers up. If the ECR in the RCM does not activate, the ECM wo'nt power up. NOW you have the Fan module looking for wakeup pulses from the ECM but not getting any - so it goes into emergency mode and runs the fan at high speed.