The tub on my Whirlpool ultimate care will not spin or agitate, but the motor seems to be running fine and it fills and drains properly. Is there any way to know wether the problem is with the motor coupling or with the gearcase without removing each one?

check the motor coupling,if the coupling is broken you'll hear the motor run but the agitiator won't move and no spin,the coupling connects the motor to the transmission.watch this video
http://www.youtube.com/watch?v=9K1KHEogf3c

The problem is most likely with the lid switch. This washer can fill and agitate with the lid up or down but will only drain and spin with the lid down. If the lid switch breaks the washer does not know that the lid is down so it will not run.

The part number for your model is 8054980 and runs about $20.00, it is shown in the image on this link below as part 11.

http://www.searspartsdirect.com/partsdirect/showSubComp.pd?imageUrl=http%3a%2f%2fc.searspartsdirect.com%2flis_png%2fPLDM%2fW0403060-00001.png

Broken cupler between motor and tranny

motor brushes would be first suspect.

Thats very agitating.There is a motor that runs the agitater,its either going out or you have lost the drive,a little spendy to have fixed.
Hope this helped.Let me know by rating me
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lenwest

motor coupler is goingto be the issue, easy enough to replace, you can find a video on you tube, search "whirlpool motor coupling"

If the washer fills and drains, but will not agitate or spin, you may have a broken motor coupling. Click on the follwing link for step-by-step instructions on how to replace:

http://www.fixya.com/support/r385252-replacing_motor_coupling_whirlpool_top

If you require part assistance, please post back with your model number (located along the washer tub opening) and I can get a part number for you. The repair cost for this item is less than $20 and fairly simple if you read and follow the instructions provided. If you require further assistance, please post back and let me know. I hope this helps you.

The spin tub mounting block is probably stripped on the basket drive. Remove agitator. Now put machine into spin do you see shaft spinning but the tub isnt moving???

It sounds like the coupling between the motor and gearbox has worn out. It should cost around $15 plus shipping and handling.

mj, sounds like a broken coupler, look at number 13 on the picture. The fact that it won't agitate or spin but will drain rules out the lid switch. This is not a hard job. Check this out first. Catriver..post back