I also have a Kenmore Series 90 washer. I'm having the same issue, except my washer agitates just fine... it just won't spin consistently (I say consistently because I think it does spin sometimes). If I "coax" it (meaning I start it spinning by hand), it will continue spinning. Just today I noticed a burning smell, but that's new. Mayer... should I start with the Motor Coupling?
I had a similar problem recently, so I took it to the Apple Store. Turns out it's a known problem. Under their "Quality Program" they replaced my power adapter free of charge! The Genius even suggested I bring in my old T-type adapter to see if it was covered. Still need to do that :)