I had the same problem with my Kenmore washer. I've talked to a few people and they all seem to pretty much use the same transmission/gearcase/whatever-you-call-it. Since the motor coupler was OK, I got brave and cracked open the gearcase. I found an exploded view of the gearcase at the Kenmore website, which I used to identify the bad part I found. It's called the gear&pinion, which is the first thing you'll see when you open the case. It had obviously worn out to a point where it would no longer engage. It's a plastic gear and I could tell it was worn out because the very top of the teeth hadn't worn at all and they stuck out about 1/8 inch beyond the worn portion of the teeth. I figured wear like this was pretty consistent with the symptom of making a loud, grinding sound and not doing any spinning. I got lucky and called a guy I know who works on washers and he had a complete used gearcase that he's gonna sell me for an unbelievable low price, which I'll not spoil the market by divulging. Good luck fixing yours. Judging by the apparent complexity of the works inside the gearcase, I'd say repairing it is probably not for most people. Call around to local appliance repair shops to see if you can find a used gearcase for a reasonable price. It's still a fairly involved job to replace it, but if you're brave enough to take your washer apart to the point of pulling out the motor/gearcase assembly, you're most of the way there already. Going with used is probably a good idea on an older machine since the rest of the washer is going to be in similar condition. It probably doesn't make much sense to put a new one in it unless that's all you can find. After all, in a few years when the machine dies completely, it will be a wreck except for the shiny gearbox.
Dale, March 2010