GE Washing machine agitator does not move during wash cycle (self trouble-shooting)

I have no experience with washing machines.
GE MODEL: GTW485ASJ1WS
UPDATE Gearbox and or transmission was busted. Cost of repair + labor would have been as much as a basic washing machine. Bought a new one.
I noticed my washing machine would not clean clothes well, and slight detergent stains would remain on the clothing after a wash. I unscrewed the magnetic key and stuck it in the locking slot so I could watch the washing process with the lid up, and of course the auger/(plastic tower thingy) would not move during the wash cycle. My washer is essentially doing a LONG soak to "wash". Using a speed wash cycle in the video for the sake of time, problem persists on other modes as well.
I also noticed that moving the auger left or right did not move the drum. I am not sure if that is normal, or if moving the auger left/right should be turning the drum...but I am not sure if that means the auger or agitator is broken, or whether its the metal spindle thinger with teeth that the lower agitator sits on is damaged, or if its something entirely unrelated below the machine. Visually, the "teeth" of the lower agitator and the spindle look ok, but I may be wrong. I would like to order a replacement part(s), but fear that it is a deeper issue - so I ask that someone more experienced take a look before I order any replacement parts or buy a new washer!
Again, I have 0 experience with washing machines.

[@jdrs4214]

I have 2 of those late model GE washers that were kicked to the curb, by their previous owners (my neighbors). I know why they were tossed out. Those machines eat up those poorly designed agitators, like a dog eats a tin can of wet dog food. (The transmission rounds off the splines on the block, at the center base of the agitator, and renders it useless.) ……and these new washing machines, aren’t the best in the world, and have nothing on the old washing machines that used mechanical timers with a servo motor hooked up with a camshaft and electrical contact points.
I took those 2 washers apart to modify the transmission shaft and the splined block at the base of the agitator. I drilled a hole through the agitator block and the transmission shaft, and threaded the hole to use a stainless steel lag screw to secure it in place, so I never have to worry about spending $75.00 every freaking year for a poorly designed piece of plastic.

[@zackamanda9799]

Would of been nice if you showed how you got the auger seperated from the agitator.

[@jdrs4214]

Repair Clinic has helpful tips on how to remove the “auger” on that washer.
It’s amazing how manufacturers now have new terminology, for their newer and inferior washing machines!!!! We now have “impellers” (a very low profile piece of plastic that moves around at the base of the spin basket), an “auger” (the one pictured here on this video), and of course, the old style agitator.
I thought an auger was something plumbers use for plumbing work???!!! Huh???

[@jns7820]

Mine is doing the same thing buddy! Haven't tore into mine yet but I suspect I have the same issue! Thanks for posting this!

[@ВалентинаУстюгова-ъ4в]

ऐऐ

[@BillTolmachoff]

Did you happen to repair the problem?