Motor is running but the paddle won't move.

In the days before electronic speed controls, speed reduction was by a number of series resistors and at low speed there was a lack of torque. Professional mixers overcame the problem by using a multiratio gearbox that wouldn't disgrace a motorcycle or a small car.

Electronic speed control allowed speed feedback so when a load is applied and the motor slows, more current would be supplied tending to maintain the speed - not perfect by any means but usually much more efficient than the old system. I don't know the precise details how the system works but I expect that is where the fault is.

Is the humming noise the sound of the motor straining to turn without moving (it won't last very long like that) or the sound of the motor turning but not operating the paddle?

Sounds like a worm gear problem to me, it's impossible for the motor (armature) to move far enough to not drive the gear. There are driving pins in the system from fuse gear to paddle.
1) in the fuse gear
2) inside gearbox above planetary joining shaft to bevel gear
3) through planetary and shaft

There is also one joining the little gear inside the planetary to the shaft, doubt you'd break that one though.

The screw under the head is for adjusting the head height for when the standard paddle and bowl are being used. First tip the whole machine upside down and tighten the hinge pin screw right up inside the pedestal post. Next reset the head height with flat paddle. Screw in is head down, screw out is head up. You want the paddle to just stop tinging the bowl on high speed.

It also has snaps that have to be popped loose in order to separate the bottom from the top it takes some force here. Even after the screws are out

Sounds like what happened to my wife's mixer. There is one nylon gear in the drive assembly that is designed to break if too much load is put on the mixer. Like what can happen with dough or butter that is too hard/frozen. That is designed to save rest of the mixer. Sounds like you need to replace the KitchenAid Mixer Worm Drive and Pinion Gear Assembly. In our case, it was not the nylon gear that broke, but a small pin that is this gear assembly. By getting the assembly & not just the nylon gear, you cover more of your bases. I found a video on line that walks you through replacing the part. I also bought the part online. The assembly part, including shipping cost me $12.95.

Hope this helps.

Obtain a copy of the Repair Part List for your model from Kitchenaid.com.
Download a Copy of the Kitchenaid Service manual.

http://www.kitchenaidparts.be/centers/servicemanual/mixer.pdf

First, you may want to adjust the mixer's speeds:

1. Loosen the lock nuts enough & Turn the 2 top screws clockwise until they cannot be turned
anymore. Leave the bottom screw alone for now.
2. Use a dab of white paint or paper whiteout to mark the positions of the Phillips screws.
3. Plug in your mixer and Set the speed selector to "Stir".
4. Turn each top screw One full turn couterclockwise (alternating between Left and Right)
Keep making one full turn at the time (for both left and right) until the motor starts running.
5. Put your hand near the Agitator shaft and allow it to brush your finger slightly. Use your
watch or clock and start counting the number of times the shaft touches your finger in
60 seconds. The correct count should be 60 RPM (Rounds Per Minute). If it is less
or more than 60, give each screw 1/4 turn counterclockwise or clockwise and start counting
again. Now tighten both lock nuts.
6. Set the speed selector to "6" and turn the bottom screw either clockwise or counterclockwise
to achieve a speed of 180 RPM.

For your reference, the planetary RPM's for the 5-qt. tilt-head Artisan Stand Mixer are as follows:
Stir speed - 60
Speed 2 - 95
Speed 4 - 135
Speed 6 - 180
Speed 8 - 225
Speed 10 - 280

Second, if the mixer won't run:
Remove the Control Plate Assembly (36), the Phase Control Board (39)
and the motor Governor Assembly (35). Inspect for loose connections,
burnt or damaged components. If they seem to look OK, re-assemble
them and test the mixer. If the motor still won't run, then I might suspect
a defective Phase Control Board (39).

When you are able to remove the paddle, feel the opposite side of the spindle. It should be smooth. The pin should not stick out the back at all. Carefully, tap it in until it is even with the spindle. That will fix you up, unless the pin itself is also damaged. If so, get a small file and remove any burrs from where the paddle mounts.

I think this link will help you understand what is needed to fix your mixer.

You will need to purchase a gear. Here is link MarBeck should have it.

You may need to replace some grease. Make sure to use a non-toxic food grade grease.

I think this link will help you understand what is needed to fix your mixer.

You will need to purchase a gear. Here is link MarBeck should have it.

You may need to replace some grease. Make sure to use a non-toxic food grade grease.