James a new motor is highly unlikely, these things are very robust. If you can't rotate the burrs by hand sounds like the bearings are seized. It should be possible to have it rebuilt and have the rotor taken out to check for coffee jamming it or if the bearings are shot. To remove and install new bearings is quite cheap and simple for any workshop.
Coincidentally I helped someone with a broken pump motor last week. The new pump leaked (they seem to come free with this feature the past few years no matter which brand) back into the motor seizing that end bearing. Motor wouldn't turn, just hummed. 20 mins to take it apart, clean it up and install a new bearing.
Someone once gave me a Major that was full of coffee inside, so much that the contactor (that buzzing you hear) couldn't switch as it was full of grounds. Same for the motor. A good vacuum, a new contactor and new bearings and it was good to go.