Not entirely sure how I'd test that. I did manually spin the transmission input in both directions and had it agitate and spin.Clutch?
I've done some googling and thus far everything I've seen as a possibility has checked good. It's a Whirlpool direct drive (Kenmore branded). Motor checks ok electrically, same with starter cap. Supposedly, if the issue were in the transmission, I'd hear strange noises when spinning manually if I could do it at all. Same with the pump. On some models, they won't agitate with the lid open so I jumpered out the switch that controls that function. The timer motor runs. I don't see any evidence of arcing or general bad connections.Go on an appliance repair forum and ask there. There's very little in a modern washer or dryer that isn't easy or cheap to replace yourself. People who buy new washers when they break are idiots.