The house has air. The air is not cold. Outside, the fan is a statue. That is a clean story.
What it usually is
The thermostat is calling (Y). The indoor blower (G) is doing its job. The outdoor section never got a useful circuit: disconnect pulled, breaker, fused whip, contactor, capacitor, or a motor that seized. None of those are a filter. A hose will not close a contactor.
What you can look at
Disconnect sitting pulled at the box on the wall. Breaker in the middle. Debris locked in the fan. That is looking. Opening the outdoor electrical cover is not looking.
Hum and no spin: stop. That motor is trying. Do not stick a screwdriver in the fan “to help it start.” That is how people keep a finger.
What we will do on site
Meter, capacitor test, contactor, spin. Written finding. A capacitor is sometimes the whole story. Sometimes it is the capacitor because the fan was already dying. You get the sentence before the part.
Toolbox will often stop early on this pattern. Book either way.