If you are getting functionality with the other elements of the system. Exhaust motor, T-stat operation etc then I would be looking at the blower motor and run capacitor.
After disconnecting power to the blower motor (pulling plug if 120v or disconnect switch) does the blower motor shaft (ie squrirrel cage fan move or is it seized up?) True, usually a hum will tell you it is seized up and a bad run cap will just not make it start (no hum and free wheeling shaft).
Run capacitors are cheap to replace just match the MFD (microfarad) rating on the side of it. BEFORE touching it you must discharge the old run cap.
1. disconnect power (triple check that)
2. take an insulated screwdriver and holding the insulated handle touch both ends of the terminals of the capacitor.
3. match the new capacitor in mfd rating and reconnect terminals.
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