Why does it hum? Because it doesn't know the words.
Sorry, bad early morning humor.
I actually would think the humming is the compressor still running as the thermostat is still calling for cooling, with the FAN having quit on you.......... Fan motor may be failing, it may have debris in the fan housing causing it to "drag" some and get hot and eventually fail, or something along those lines.
Anyhow, it sounds as if pulling the outside shroud off and took a look (or having a trained professional do that) would be next. Be careful - on a ladder, on the AS if necessary, running the unit with the shroud off, all that can be dangerous.
Hope this helps.