One of the many fine techs here at Appliantology posted his story with a Maytag washer that wouldn't spin in the Appliantology forums.
The initial situation in his words:

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Problem Statement (State what is the appliance doing that it should not be doing, and what it's not doing that it should be doing.): In any cycle or option motor only hums, no agitation no spins

 

What diagnostics have you already done?: - Washer powered on normally.
- Motor would hum but not rotate in spin or agitation.
- Error code F7E1 logged.
- Motor could turn freely by hand.
- Basket and gearcase not locked
Motor winding ohms: Old motor showed imbalance. New motor installed, same symptom.
- Control board voltage output: Red ↔ Black = ~120 VAC, Red ↔ Orange = ~120 VAC, Black ↔
Orange = 0 VAC. Proved one leg missing, initially pointing to bad driver.
- Harness inspection: Continuity checked, no opens found. Still suspected under-load failure.
- Direct motor test via harness + capacitor: Motor only hummed.
- Capacitor testing: Tested 'good' on meter but suspected weak under load.

On top of this, there was one more strange symptom:

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One thing I forgot to mention is that with the washer in standby mode, with all lights off, the thing would try to spin and turn itself on.

Given this strange behavior, he was understandably thrown on how to proceed.

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The capacitor tested good, then I checked the motor ohms, which were a little out of spec, so I replaced the motor, as I couldn't be sure without information from Maytag. The problem persisted. Then I went for the main control. I tested the UI and knew it wasn't the issue. The main control puts out a simulation of 3-phase AC voltage by pulses, per the service manual that I acquired from SM, which is the only great source I know for tech manuals. After verifying that one leg was missing voltage, I decided to replace the control, but the symptoms remained.

After changing all those parts, no resolution! But finally, he found the issue:

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My goal is to help whoever may encounter this problem, a $30 part was the only problem.

- Weak run capacitor failing under load. - Measured fine on a multimeter but collapsed when driving current. - Created imbalance that mimicked a bad winding or bad board. - Replacement restored proper motor operation

Resolution:

 - Installed new capacitor (OEM spec 45–50 µF). - Reinstalled old motor. - Performed DLMS calibration via service mode. - Motor ran normally in agitation and spin, kept the new control as it looks slightly different with some missing ceramic capacitors, but according to Maytag it was the replacement for a 2 years old washer control.

Lesson learned 

Lesson learned indeed! And thank you for sharing your hard earned lesson with us. Now we all know what to look out for when we encounter a similar issue in this model.