First off...did you check your wiring to see if a wire is shorted to another wire, part, or frame?
I removed the motor assembly with the spindle. No need to seperate the electric motor from this assembly. Spray it with a cleanser and wipe off what you can on the chrome areas. The stubborn areas I soaked in a bucket of Simple Green. I hung the motors off of a rod that I attached to a bucket. I did not submerge the motor. Just a few of the chome tiers. I wasn't sure if this would damage the bearing but apparently it didn't on mine. Soak at your own risk. Don't let water get into the top of the chrome. Then I just cleaned the rest of it with whatever worked. I used a dental pick type tool to remove the old crud in areas a rag couldn't get into. Afterwards, I resoaked the same area in a bleach solution. I used rags to go over all of the chromed area and then I rinsed everything well. Do not soak the whole motor and windings. I did use Q-tips and damp paper towels to clean the motor itself.
The brushes are graphite or carbon blocks that allow current to pass through between the stationary and moving parts. Hamilton Beach is of no help on parts. I know it is over sixty years old but you think that they would still have the specs. Best thing to do is buy some brushes and file them down. It is a long process. Some sort of machine would be nice but I only had a file. I used a fine smooth flat file, laid it on a table, placed the brush on its side and moved it back and forth so many times, flip it over, do the same to the other side so it will wear evenly. There is a metal shunt, spring and wire, that you want to keep centered. You want to apply pressure evenly so the brush wears the same on each side. Be careful not to angle the brush as you are filing it. I had a caliper to measure the original width. Just keep filing until you have reached your measurements. I was off by .002, but I still managed.
It is a long and tedious process because the brushes are really hard. I'm sure there are easier ways, a machinist, maybe a belt sander, but I had my trusty file and a lot of time to waste. I only made a set for the center one. The left and right ones had plenty of material. I bought the closest tolerance from McMaster Carr, my favorite store, but after they were delivered I looked at the brush manufactueres web site and there were some a lot closer, less filing. Ace hardware sells motor brushes too. The ones that I found were the proper size on the shunt and two of the three dimensions. This is what I bought.
65705k37 - Carbon Brush W/Spring & 1-7/16" Shunt, 1/4" Thk X 1/2" W X 13/16" H
When your brushes are ready, put them in and set them by running the motor on low. Run it only at low for awhile. You will see some noticable sparks. When they become less intense and more evenly distributed, then run it at medium and then high. You want the flat brushes to wear down until they are curved and match the commutator, the round thing that is spinning against the brushes.