Here is how it works:

The ECU sends pulses to the Fan Module. (A narrow pulse is just an "Are you there?" message, a wider pulse tells the FCM to run the fan, the wider the pulse, the faster the fan is to run.)
The Fan module responds with an "I'm here" pulse.

If the Fan Module does not get pulses from the ECU, it puts the fan motor in emergency mode, and the motor runs full speed.
If the ECU does not get the "Im here" pulses from the Fan Module, the ECU lights the little "radiator" light that people think is the low coolant light.

It is that simple. If you have a fan motor running fast with a "radiator light" on, you have a breakdown in communication between the two modules. This is usually a sign of a bad Fan Controller.

If you have a fast running fan and NO light on the dash, it means the fan module is telling the ECU that things are OK but still running the fan too fast - change the Fan Module.
Or.....
If you have a fast running fan an NO light on the dash, it COULD mean the ECU is bad but I doubt it.

I'm leaning toward a bad Fan Control Module at this point, but if you dont even know if there is a light on the dash, I can't really help you, as you are not providing enough information. One thing is sure, I'd not change the ECU until I'd exhausted all other avenues. ECUs simply don't fail very often.