My blower in my central air conditioning is not working properly. Everything else seems to be working. I turn off the power to the unit and took of the cover to get to the blower, everything looked fine and the blower turns smoothly, but I noticed a slight burning smell. I turn the power back on and noticed the blower is getting power but is making a decently loud buzzing noise. Then I try turning the blower with a little pole and noticed it wouldn't move like something is stuck preventing it, but when the power is off, it turns fine. What's going on?

Seems to be a rash of these, likely the starting capacitor. Here is what I just told somebody with a no start inducer:
There are pictures of capacitors for larger motors in the sticky at
https://www.askmehelpdesk.com/heatin...ons-58313.html

A bad capacitor is a frequent cause of a motor not starting. If you have an ohm meter, you can do a rough check of one. Short the terminals with a plastic handled screwdriver or something, and remove one. Watch the meter as you connect the leads. The reading will jump to a high value and then climb off scale for a good one. If it is bad, you can note the info on it, but might better take it out and to a electrical or HVAC supply and let them match it.

Motors usually have nothing inside to fix, but the capacators are a cheap, easy fix.

I think the bearings have gone bad. Once a magnetic field is generated the rotor is being pulled into the stator, that is why it moves hard when energized and smooth with no power applied. If it where the start capacitor, once you gave it a push it should find its way and run like normal, most of the time. I'm also guessing this in not a belt drive motor.