DIAGNOSIS A loud hum without movement means the motor is getting power and trying to run, but the drive mechanism isn't engaging. The most common cause is the door being manually locked or, more likely, the emergency release cord has been partially pulled, disengaging the trolley from the opener.
FIX Look at the red emergency release handle that hangs from the trolley on the rail. 1) If it's pulled toward the door (downward), the trolley is disconnected. 2) To reconnect, lift the door manually until the trolley slides back to meet the opener's carriage. You'll hear a click. 3) Now pull the red handle straight back (toward the motor unit) until it latches. You should be able to operate it normally with the remote or button now.
IF THAT DIDN'T WORK If the release cord wasn't pulled, the problem is internal. The drive gear might be completely stripped (see the grinding noise issue) or the motor capacitor might be failing. A bad capacitor gives a loud hum but not enough torque to start moving. This is a more advanced repair involving testing or replacing the start capacitor mounted inside the motor housing.
HEADS UP Don't let the opener hum for more than a few seconds. You can overheat the motor. If reconnecting the release doesn't fix it, unplug the opener and investigate further to prevent damage.