Blower motor failure. The blower motor is responsible for forcing air through the heater core and out the vents. If the blower motor fails, the fan will not work at any speed.
Switch failure. The switch is responsible for turning the fan on and off and controlling its speed. If the switch fails, the fan will not work at any speed.
Wiring issue. A problem with the wiring can prevent the fan from working at low speed. This can be caused by a damaged wire, a loose connection, or a short circuit.