The 3 most common part(s) or condition(s) which cause the symptom Washer won't agitate are listed below starting with the most likely. Check or test each item and watch any available videos.
RepairClinic Item # 1264702
If the washer won't agitate the drive block or bell might be worn out or broken. The drive block connects the washer transmission to the agitator, if it's worn out the transmission shaft will still move back and forth but the agitator will either stay still or move slightly.
RepairClinic Item # 3481
If the washer won't agitate the drive belt might have worn out. Over time the drive belt will fail just from normal use . Replace the belt every two or three years depending on how much the washer is used.
RepairClinic Item # 1195901
If the washer won't agitate the drive motor might be defective. This is not common. Check all of the other related parts to this symptom before replacing the motor. If the motor is visibly burned out or physically damaged it will have to be replaced.