Diagnosing DC motor failure
Try new brushes before you buy a new motor.
You report a large amount of carbon dust so the brushes may have worn down to a point where they no longer make effective contact with the commutator. Typically they will be spring-loaded. As they wear down the springs extend and exert less force on the brushes, leading to a higher resistance contact. As you have a low voltage supply trying to push a large current through the motor you can't afford any significant voltage drop across the brush-commutator interface.
Your motor manufacturer may document a minimum length for the brushes in which case you can check that. Otherwise just try some new brushes. You don't seem to have any other obvious motor faults. Basically brushes are a wear item for a brushed motor and you should expect to have to replace them periodically.
I've successfully repaired a non-working motor by replacing the brushes. Other than being shorter than their replacements the old brushes looked in perfect condition - they just didn't work.