That circuit is kinda cool...

As Alax said, the fuse provides power to the Fan Control Module (FCM). The FCM then supplies power to the fan motor, under command of the Power Train Control Module (PTCM or PCM),

It works like this:

There is a single wire running from the PTCM to the FCM. This wire has 12 volts on it, the PTCM pulls this wire to ground in a series of pulses, the WIDER the pulses, the faster the FCM makes the fan run. (It does this by sending pulses of 12 volts to the fan motor, your meter will show 4 to 12 volts, but that's because your meter is averaging the pulses - DC motors are not usually run on low voltage for low speed, they are run on NORMAL voltage that is pulsed to get the right speed). Periodically, the FCM also pulls the line to ground - this tells the PTCM that the FCM is still working. The PTCM turns the light on if it does not see the pulses coming back from the FCM.

Also, if the FCM does not see the pulses from the PTCM, it assumes something is wrong (which is the case) and that the engine's temperature is unknown (which is also true) so the FCM turns the fan on all the way. If the light is on and the fan is running full speed, there is a communication breakdown between the modules.

If the light is on and the fan is not working, then the big fuse to the FCM is blown OR the FCM is bad. (I do not think the FCM can sense a bad fan motor.)
You can always unplug the fan motor from the FCM, the connector is clipped to the radiator support on the driver's side - use wires with the end stripped off and see if you can jumper the fan motor directly to the battery. If the motor turns, the FCM is bad. If the motor does NOT turn, the motor is bad.

But I'm pretty sure you have a bad FCM or blown fuse, given your story here....