Our pre 1995 kenmore top loading washing machine doesn't work, 90% of the time the clothes are sopping wet. I suspect the spin cycle is malefunctioning. And it often makes a loud bumping noise.Does anyone know the how to fix this, or what is causing it?

It sounds like it is spinning but out of balance which will eventually shut off the spin cycle. You;ll need to balance the load and watch the spin cycle to see if its not spinning fast or not pumping out the water. They are 2 separate parts of the spin cycle.