Yank that motor off and take it to ye old local electric motor shop. Preferably the mom and pop type that some guy started in his garage back in the 60's type. They can test it in a couple of minutes and repair prices are dirt cheap. If it's toast they will likely be the best place to get a motor from as well.
A fella I know gave me an old heavy duty grinder from his father had kicked around with forever back in the 60's. It didn't work and cord was all cracked. Nice grinder though and made of that exotic metal called "heavy steel", long extinct from the consumer arena. I took that to the local electric motor shop and the guy tossed in a capacitor , I replaced the cord and it is perfect after cleaning up some. Cost me $17. The guy told me those old motors, unlike most of todays light weight Chinese trash can be rebuilt over and over. I have taken a couple others in over the years and he didn't even charge me to test them and it only takes a minute.