I too have a Kenmore Series 80 and have a similar problem
... but slightly different.
At the end of the wash cycle, I find the clothes still very wet and you can tell it didn't spin since all the clothes are just at the bottom (not stuck to the wall of the drum).
This happens intermittently. Sometimes it spins, and sometimes it doesn't.
When I do find it didn't spin, all I have to do is turn the timer all the way around back to the spin cycle. When I do that, the thing spins (everytime!).
What do you think is the issue in my particukar case?