AAV7000AWW washer fills, does not agitate, drains and spins ok. transmission shaft does not spin during agitation portion of cycle

Your washing machine top lord or front lord?
If your washing machine top load you have cleared drain valves in have blocked then check drain motor like that as you can check which model or type

Question edited for clarity 'make model (what it is).
Question moved to Frigidaire Washing Machine.

This is the Transmission unit, which I would say puts it beyond economical repair.

Frigidaire H Transmission #WCI-134735700
List Price: $765.13
Sale Price: $637.61

On first reading, I thought it sounded like the pump, but then no agitation, but it spins. This makes it sound like the control board. In view of the confusing actions and the cost involved, I would call out a Service Engineer.

https://www.partswarehouse.com/Frigidaire-FEX831FS2-Washer-Dryer-Combo-s/70205.htm

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Depending on the brand of washing machine, the agitator may be a single piece unit or a two piece dual action agitator. If the single piece agitator or the lower portion of a dual agitator does not oscillate back and forth during the wash cycle, or if the agitator can be turned on the transmission shaft, then the spline may be damaged and the agitator may need to be replaced. Most agitators are held in place with a bolt that threads into the top of the transmission shaft and is located below the softener dispenser or top cover. Some models use a small set screw in the barrel of the agitator just above the base to secure the agitator to the shaft, while some will use a rubber o-ring to provide a tight fit. When the retaining device is removed you should be able to lift the agitator from the shaft.

The clutch assembly works only to release the basket allowing it to spin during the drain and spin cycles. The drain function works only when the spin function works. If the machine also agitates during spin cycles, then the problem is in the transmission assembly not able to release the agitate gear from the agitate spline in the drive shaft.

sounds like the washer transmission has failed.

It doesn't agitate If your washer doesn't agitate, check these:

Lid switch
Motor coupler
Belts
Clutch
Drive motor
Drive pulleys
Transmission
Agitator
Lid switch If the lid switch is defective, the washing machine may not agitate or function at all. The switch is inside the washing machine main housing near the door frame. Often you have to raise or open the top or front of the washing machine to get to the switch. If it's defective, you need to replace it. 

Motor coupler Many washers produced by Whirlpool® use a small, relatively inexpensive motor coupling. It's plastic and rubber and is mounted to the shaft of the motor on one side, and to the transmission on the other. Over time, the coupler wears out and fails. If this happens, you need to completely replace it.

Belts Many washing machines have one or two belts. If a belt is broken or badly worn, you need to replace it with a genuine belt from the manufacturer. (Some washing machine belts are designed with special characteristics not found in automotive belts.)

Clutch If your washer was made by GE®, it may use a clutch for agitating the clothes. As the clutch wears out, it may prevent the washer from agitating well or at all. If the clutch is worn, you need to replace it. For this job, you probably want to hire a qualified appliance repair technician.

Drive motor Many washer brands use a reversing motor. For agitation the motor runs in one direction, for spinning and draining, the other. It's possible for a motor to burn out in one direction and continue to operate in the other. If this happens, you need to replace the entire motor. 

Drive pulleys The motor or transmission drive pulley may be worn and unable to turn the drive belt. If so, replace the pulley.

Transmission The transmission could have either of these problems:

• Older washers produced by Whirlpool® have a transmission with an electro-mechanical shifter. If the shifter becomes even partially defective, the unit may not agitate properly or at all.



• The transmission may have a worn or broken gear, or some other internal problem.

If you suspect a transmission problem, you may have to call a qualified appliance repair technician to repair it.

Agitator The inside of the agitator--where the transmission shaft attaches--can become worn, and strip out the spline that allows the agitator to properly grip the shaft. Then the transmission shaft rotates back and forth as it should, but the agitator doesn't move properly. If this happens, you may need to replace the agitator and/or the transmission spline.

Motor coupler between motor and gearcase.

It is either the inlet velve or the cycle programmer faulty

the lid switch is fine. check wiring and motor connections.it could also be a bad timer

Well, it sounds like you've done your homework. My first suspect would have been the agitator dogs too, but you said they were fine. Another likely suspect would have been the motor coupler, but you said the washer spins during the spin cycle. If the coupler was bad the unit would fill, but wouldn't agitate or spin. Plus, it would make an awful noise. I would have also suspected a clutch assembly, but you said the wash tub can spin. Normally, when the clutch goes bad, the drum won't spin, or spins slow. Another suspect could have been a bad lid switch, but the washer would have filled and stopped, without agitating or spinning. The only remaining suspect that I'm aware of is the gear case (transmission). Checking under the washer can give you some clues. Normally, when a gear case starts to go bad, they leak an amber colored oil. You may find puddles or drips under the washer. If you see no signs of oil the gear case could still be defective, however. But, before you go through all the trouble, double check the agitator one more time. Completely remove it from the tub and check the under side to ensure the grooves that grip the top of the gear case shaft have not been worn smooth. I hope this may have been some help to you.