Sump Pump won't pump; how to fix?

Did you prime it to get it sucking? Small pumps will often need to be primed, especially if they were sitting dry for 20 years.

Honestly, I am surprised that the motor is humming in the first place – after 20 years in a box, I would have expected the oil/lubricant/grease inside the housing to have dried out.

Unplug it and try turning it by hand a few times until it loosens up. The armature lubrication can be dried out like @elbanditoroso suggested.
If nothing is moving the humming you hear is the motor trying to turn. That is a good sign. Don’t toss it yet. See if you can find the reset button. You’ll need it if the motor goes over temp due to the stalled condition.
You might have to turn it with a screwdriver wedged into the grill.
Does it have accessible bearings that need lubrication? A couple of drops of 30 weight oil might loosen it up.

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If it’s humming but not pumping the bearings are probably seized. Turn it off, and try to turn it by hand. If it doesn’t turn, it’s toast. 20 years old? You got your money’s worth.

Can you turn the rotor by hand? If so then that’s good. There is typically a motor start capacitor and they have a shelf life (electrolytic) That’s my guess considering it sat for 20 years. When they go bad the motor will sit and hum like that. Don’t let it do that for more than a moment. It’s pulling high current when it does this and it will eventually burn out your stator if you let it continue. The capacitors are easy and cheap to replace.

I replace the start/run capacitors on my AC unit every five years as a precaution for reference. I always find they have degraded a little in that time. Most people let them run to failure and they will usually fail at the worst possible time.