Kenmore Washing Machine Question

I have a Kenmore washing machine that was purchased in 1988. The agitator is making a grinding noise and partially 'slipping' as it tries to do its thing. The suds also don't get completely rinsed away on a normal cycle. I have the parts list and diagram for the unit, model # 110.82892300, Kenmore Advantage. If I had to guess, it seems like there is something wrong in the gear case, part number 389246. It has several gears with teeth, and the sound the agitator makes might be these teeth slipping.
I may have already answered my question, but does this seem like something work repairing, or should I just get a new unit?
While I am posting, I had just changed the input hoses to the washing machine, and then on the next cycle, the downstairs powder room toilet bowl filled up with suds! The toilet is directly below the washing machine, so I guess there might be some partial blockage below where the two drains meet, and then when the washing machine empties, it backs up into the toilet bowl. Not that big of a deal, and it keeps the bowl clean! It doesn't overflow or anything, so is this something I should call a plumber for?
Thanks!
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Is the sound coming from the bottom of the appliance where the transmission (gear case) is or at the top where the plastic agitator is??
You're model has a 2 piece agitator and it is common for the agitator 'dogs' in it to wear leading to noise. It usually has nothing to do with the transmission. You can see an agitator repair kit for your model which includes the 'agitator dogs' at the following link and read about replacing them at the second.
http://www.appliance411.com/data.php?rc )21
http://tinyurl.com/2lmzp

Maybe you're using too much detegent for water conditions, there a problem (partially plugged, kinked, etc.) in the drain hose or connecting hoses or pump?

It definitely has nothing to do with the washer but *might* be the cause of the washer's draining problem?
Dan O. - Appliance411.com http://ng.Appliance411.com/?ref411=Kenmore+washer
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Thanks, Dan. If the dogs are worn, does that lead to the agitator "slipping" as it tries to spin the clothes? That's what is happening with the unit, and if it is just worn dogs (love that phrase), then it seems well worth repairing.
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The top section of the agitator is often referred to as the "clothes mover". If it is slipping, the clothes will not move properly through the water and not clean well.
If the *base* of the agitator is not moving, the agitator dogs have nothing to do with that. That could be caused by a worn agitator bas or a problem in the transmission.

I would think so.
Dan O. - Appliance411.com http://ng.Appliance411.com/?ref411=Kenmore+washer
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Dan O. wrote:

the two sections of the agitator - it commonly leads to that kind of noise complaint.
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A 16 year old washer is not worth spending much on repairs. Get a new one. Des

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