When I turn on my central air/heat, I get a buzzing sound from the furnace
unit. The outside AC unit and the gas heater seem to be working but the
blower fan (below the inside furnace unit) will not move.

I removed the blower from the furnace unit and the blades spin very freely,
no sound whatsoever. If I set the thermostat to "fan only" I still get a
fairly loud electrical buzzing sound, like something is trying to come on,
this is even with the blower physically removed from the unit.

I've done some looking on Google and seen other accounts similar to mine
where the capacitor that serves the blower is bad. I'm not sure if I have
that stated correctly, but any suggestions on how to proceed would be
appreciated.