The first thing to check when the fan in your window unit isn't running is the power supply to the unit. Verify that the power cable is plugged in. If the unit is plugged in and not running, see that the power breaker for the socket hasn't tripped at the main circuit breaker. If you have a number of other appliances working in the room with the window air conditioner, this can happen sometimes.
If an object becomes trapped in the fan, it can keep the blades from moving. Disassemble the cabinet so the fan can be examined. Clear anything that might be stuck in the blades. Sometimes dust, lint and animal hair can gather on the fan hub, causing it not to move. In this instance, the fan assembly should be removed so the hub can be cleaned.
When the motor for the fan burns out or fails, it won't move the blade assembly. The motor is usually located in the hub of the fan, and wires connect the motor to the main circuit board. Replacement fan motors can be ordered from the manufacturer, or you can find another model by shopping online or in specialty electronics stores. While the fan is out of the window unit, use the opportunity to clean it up.
The control board is the brain of the air conditioner. This is the circuit board that controls all the functions of the window unit, such as coolant circulation, temperature, timing and the fan motor. If the window unit is plugged in, the power is okay and the appliance still fails to come on, the control board might be the culprit. Although these are possible to replace, replacing the entire window unit may be easier.