Computer fans with 4 wires don't have a fixed rotation speed, they adjust their speed based on a signal that comes from the motherboard or the video card.
The four wires have the following purpose (they're not necessarily in this order in the connector):
1. 12v input (powers the circuitry and the motor of the fan)
2. Ground
3. Speed sensor (the circuitry on the fan tells the motherboard or video card how fast the fan spins through this wire, by sending two pulses for every rotation to the mb/video card
4. PWM - a cable through which the motherboard (well, a chip on the motherboard) tells the fan to adjust its speed.
The PWM is short for pulse width modulation - think of it like a on/off switch. The motherboard tells the fan 60-100 thousand times a second to turn the fan on or off ... by playing with the periods of time the fan is on and off, the speed changes, because even when the fan is off, it still spins a bit due to inertia.
You can force the fan to always stay at 100% speed by disconnecting that PWM wire from the connector on the video card. I can't be 100% which one that is, but usually 12v is a red or yellow cable and ground is a black cable. The other two wires are the sensor and pwm wires, and nothing bad will happen if you disconnect the wrong one.
In worst case, if you disconnect the speed sensor, the video card won't turn on because it won't be able to know if the fan works or not, and will protect the processor on it from overheating. If this happens, you can just connect the wire back to the connector.
But anyway, the 100Hz hum is more indicative of a bad input to the speakers but I have no clue why it would change if you put your fingers there. Maybe you shield the audio cable from pc with your hand without realizing?