The Kettle Agitator gets stuck. Appears the Rotating Center is Wobbly. . .

This is a hard symptom to troubleshoot, it can have many different causes.
1. Is the stire wire in the kettle straight and spinning freely?
2. Does the agitator shaft spin freely in the crossbar?
3. Is there a small needle bearing on top of the spur gear attached to the kettle? it is a small metal circle that spins independently of the agitator shaft located ontop of the kettle spur gear, it can fall off.
4. The plastic block in the cabinet roof that has the motor spur gear coming out of it, is it cracked?
5. Does the motor turn when the switch is turned on with the kettle in the dump position?

All of these can lead to an answer of why the agitator stops turning while popping.

Is it stuck in the center agitator or the out tub?

Possible that the drum agitator bearings are off track or worn out. Please check these links for support.
Check this link :http://www.espares.co.uk/advice/washing-machines/a/7/1210/wobbly-washing-machine-or-tumble-dryer.htmlForreplacement of bearings check for tips on this visual link: http://www.espares.co.uk/advice/washing-machines/a/7/1401/how-to-replace-the-bearings-on-a-washing-mach.html

Check the wires to the heating element inthe kettle.

The agitator bolt may be loose, or the dogs may need replaced. The following link explains how to access and repair:

http://www.fixya.com/support/r823955-replacing_agitator_dogs

You can view what agitator dogs look like at appliancepartspros.com. Just type in your model number and look for item 18 under the Agitator, Basket and Tub heading. A replacement kit only costs about $5. For a bit more, you can purchase the entire agitator repair kit for about $11 (item 22). The exploded view diagram can also assist you.

Your agitator has a cap that comes off the center post, followed by an air gap cap inside. The air gap cap just pulls out, exposing the agitator bolt. The upper portion of the agitator (called the "auger") will lift off once the bolt is removed.

NOTE: Make sure when you reassemble the agitator that you remember to reinsert the air gap cap and that the rubber o-ring gasket is intact. Without it, water will eventually work into the gearcase (transmission). Also make sure you do not overtighten the agitator bolt. Doing so may damage the agitator or restrict its movement. Tighten until snug.

If you have any questions, please let me know. I hope this helps you.

Odds are that the problem is not with the belt or the pulley, but with an agitator (rotating brush) that isn't turning freely. Remove the rotating brush and check to see that it spins freely. If not, you would either need to disassemble it (removing the end caps) to see if removing whatever hair / diebris is stuck between the end caps and the body of the agitator, and if that doesn't cause free rotation, then it means your agitator bearings are likely bad which means you will need to replace the agitator assembly.

To repair agitator remove the top of it < snaps on> then remove bolt from center and the agitator will split in middle. You'll find a center cogg with three arms remove this and replace with new one< the kit that you described is this part > and assemble it.The coggs are move freely to engage so you don't have to align them in any way.

Likely a broken dog itself was making the noise. They should all be replaced.

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remove agitator top remove 7/16 bolt to remove agitator. tub mounting hub may be worn which allows the tub to drop down. the hub is located on the center post below the agitator.

If you remove the center cap from the agitator there should be either a bolt or a square recessed socket that you can attempt to tighten. The bolt is either 7/16" or 1/2". The recessed socket can be tightened using a 3/8" to 1/2" socket adapter.

Make sure the agitator is seated properly on the center post. You can accomplish this by finding the mounting bolt and loosening it enough to free the agitator on the post and push down evenly on the bottom flanges at the base of the agitator where it meets to bottom of the tub.

Try this and let me know if it helps. Post back if you need further assistance.