I have a hunter "original" ceiling fan-the heavy cast iron model-at high speed it runs but slowly at medium speed it barely turns and at low speed it won't turn at all even though motor is still running

<Moved from Home Electronics> - KISS

Most likely the capacitor. Could also be switch. Parts usually available at CeilingFanParts.com Home

Have you oiled it recently?

Oiling your ceiling fan - Ceiling Fans N More