[alloro]

You could disconnect the two wires going to the fan and connect them to a voltmeter. Turn the ignition on and watch the meter for fluctuations as you cycle through the fans speeds. If it fluctuates it's the switch, speed resistor, or a problem within the wiring.

If that is inconclusive then you could connect two wires from another power source within the vehicle (the fan will only run on high) and see if the fan runs intermittently. If it does, then you have a bad fan motor. Considering the squeal I'd lay odds that it's the fan motor.