Verify the motor is getting power from the wall. A motor will never not have power unless the connection from wall to motor via the power cord or on/off switch is faulty. Check those. The burn marks you see on the commutator is normal, its from the carbon brushes as the motor is run. If it is excessively black, that is typical of a machine used hard and will need its commutator polished and new carbon brushes to restore electrical contact.
Other typical things in a 80ish year old vacuum would be old oil or grease that has gummed up into a gooey tar, parts being stuck in place from sitting for decades on end, and just needing a full tune up overall. No sense in throwing out perfectly good motors, and you cannot find motors for antique vacuums at the drop of a hat either.
Good luck! Many people here know motor repair and would be more than happy to help, I'm sure