The Outside Unit is working fine. The inside Unit fan won't come on and makes a humming noise.

Could be a capacitor.
With unit powered down, I would see if motor spins freely.
Froze bearing?

Like start said, could be a bad cap, or a bad motor. Capacitors are cheap, so you could start by getting an exact matching capacitor and replace it. If problem still occurs, a new motor it is. Run caps for these motors usually run between 5 and 15 bucks, so you aren't really out much in doing this test.