The sound you are taking to be the motor could be the water valve trying to fill for rinse. If the cold side of the valve is clogged (debris and scale can clog the screen) and the machine is set for cold water rinse, it will stop the cycle from completing. Some machines ONLY have cold water rinse. Listen to the sound with your ear close to the fill hoses and you may find the culprit to be the water valve. This model also is equipped with the "actuator" that senses tub spin and shifts between agitate and spin part# w10006355, if the cold and hot side of your fill valve is OK, I would suspect this part next as it is the source of many odd symptoms on this model!

Thanks for the info, Nater. I'll check as you suggested when I get home from work. This washer does, in fact, only have a cold water rinse. Just to be clear, should I remove the cold water hose where it attaches to the machine and check for debris there?

There was no blockage in the hot or cold hoses. In my original post I stated that it sounded like the motor continued to run after the wash cycle was complete. I think "churning" would be a better way to describe what I'm hearing. It's similar to the sound the washer makes during the spin cycle, but the tub is not spinning. Should I try replacing the actuator? And is there any other part that could be causing this problem?

Oh, one more thing. My washer has a separate setting just for "rinse and spin." I was able to fill the tub at this setting, but the agitator would not engage and the tub would not spin. When I switched the machine to "drain and spin" the water drained from the tub but it wouldn't spin at this setting, either.

Please note that the washer works fine during the wash cycle. The problem starts at the beginning of the rinse cycle.

I replaced the actuator this morning and my washer runs like new. Thanks for pointing me in the right direction, Nater.