The 2 most common part(s) or condition(s) which cause the symptom Microwave exhaust fan not working are listed below starting with the most likely. Check or test each item and watch any available videos.
RepairClinic Item # 2666328
If the exhaust fan does not run the fan motor might be bad. Remove the fan motor from the microwave oven and see if the blades can be turned by hand. They should turn very freely, if they're stiff the fan motor will need to be replaced. The fan motor can also burn out. To test this use an Ohm meter. The motor should have continuity. If it doesn't, replace it.