Grinder hums but won’t run. Capacitor seems good, and so do windings

My Grandpa gave me a bench grinder recently to fix. He said he was using it a lot, grinding and grinding, then he heard a pop, and it stopped working. Now it just hums, and starting it by hand doesn't work.

I think it's a capacitor run motor, but not 100% sure.

There are 2 windings, and a capacitor in series with one of them, I belive it is 6uF. I charged that capacitor up with 32 volts and it seemed ok.

It did discharge kind of quickly, but that's most likely just because it's so small, and the multimeter I was using is discharging it a little. I also put a digital ohm meter across it, and at first, it started at low resistance, and slowly went up, and then it jumped to open circuit and stayed there. I'm guessing that was just because it was a tiny bit charged yet.

I saw somewhere it was supposed to start at 0 and go up and then drop off and go back to 0 and repeat if it's good, and it's not doing that.

But how is that supposed to work? If the ohm meter is applying DC voltage on one side and measuring on the other, shouldn't a good capacitor get open circuit like I did?

There shouldn't be any capacitive coupling across it with a DC voltage.

I also measured the resistance of the windings, and the one with the capacitor measures 38 ohms, while the one without it measures 27 ohms.

Is one of the windings shorted or burned out or will a new capacitor fix it? Thanks!

Edit: I found a cap with the same value in an old fan my dad had lying around, and it didn't work. One of the windings must be shorted. It's probably not worth rewinding, I can buy a new one for $35.

Edit: just took it apart to get to the motor.

Yeah. I don't think that's gonna run again without rewinding.