If your indoor fan isn't working it could be several things. We will go over a few things to check before calling for service.
First make sure there is power to the indoor unit and that a switch or breaker isn't off. Then make sure your air filter isn't blocked. Sometimes that is the only problem. Some customers don't even know they have an air filter and it has never been checked. Try setting the thermostat fan switch to the "on" position. Feel for air coming out of the vents.
If it is in the air conditioning mode, check for ice around the evaporator coil and refrigerant lines at the indoor unit. If the coil froze, the fan could be working but the air wont go through the ice until it melts. If the fan isn't working, that can cause the coil to freeze. If the coil is frozen, shut off the air conditioning immediately. Then check-out our page on heat pump iced-up in summer. (Even if it's not a heat pump.)
Some equipment still uses belt driven motors. Mostly furnaces only, not heat pumps. Sometimes the belts wear out, crack, and eventually break. If you take a look at the blower section of your heating system it is quite easy to see if you have a belt driven blower motor. You will see a motor sitting on top or next to a larger blower wheel connected by a fan belt.
Most fans are energized by a fan relay. This is probably the most common cause. The contacts inside the relay go bad. They usually stick open, never sending the signal to the motor. This is much easier and cheaper to repair than a motor going bad.
Of course, the motor can always go bad. Sometimes the bearings seize. Or the motor just burns up or weakens.
Below is a list of possible causes and things to check.