If the fan refuses to run and the coolant light never comes on, I'd read that as either a bad ECU (never happens) or a bad FCM that lies to the ECU and tells it all is OK, but it's an FCM that is not actually operating the fan. I've seen ONE FCM do exaclty that, but most of the time, the coolant light comes on as the ECU knows the FCM is not really working.

Also, keep in mind that light is a light bulb, if it is burned out you have no way of knowing. Also, the cooling system is not part of the emissions, so no "Check Engine" or diagnostic code will be generated.