Buzzing Sound From Central Air Unit - No Movement

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.
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It's the transformer. Most have screws on them that can be tightened/loosened to get the noise to stop. If it continues, you may want to reoplce it. It probably isn't going bad, just annoying as hell.....

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Ok but it's not just noise, the blower will not move.
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If the buzzing is coming from the blower (I assume that's what your are implying) then it's not a transformer and it is probably, as you hypothesized, the motor starting capacitor. It is located on or in the motor. It could also be a bad motor.
Jim Devereux wrote:

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No, the buzzing is not coming from the blower. That was my first thought but I hear it even when the blower is disconnected.
I don't mean to say that the buzzing sound is abnormal -- I heard it even when everything worked. It's just the normal sound of my central air kicking on. Only now the blower does not turn.
So...
I'm assuming I have to check the blower motor to see if it's dead, and also check the capacitor.
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Check to see if power is coming to the blower leads. If it is a multi-speed blower you have to check the leads for the speed which is wired in. If power is present, it's a pretty good shot that there is a problem in the blower.
Jim Devereux wrote:

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I checked the power leads that serve the blower motor and they do have power. I checked the 3 wires on the motor itself for continuity with the RX1 Ohm setting on the multimeter and got these results:
about 5 ohms between red and blue
infinity between white and red
infinity between white and blue
I'm not sure if these results mean that the motor is bad or not. I still can't find a capacitor anywhere, maybe this motor doesn't have one. I'm assuming it will look like a small tin can with three connectors on top.
The unit is a 'Trane' and was new in 1982. The motor is very diry with that spongy brown dust stuck into about every nook and cranny. I don't know how long these motors last, is 22 years the life span?
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I think that furnace has gotten everything out of that blower it could. In other words, the motor is probably shot.
Replace the motor, but look at the condition of the furnace. Twenty-two years is near the end of the life expectancy of that furnace.
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