We have a kenmore 80 series washer that won't go into the spin cycle but it will wash and rinse just fine

The lid latch that keeps the machine from spinning when you lift the lid may be in need of replacing. My machine would wash and rinse OK but no spin cycle until I had the switch replaced.

I have a Kenmore front loading washing machine. Yesterday went through wash cycle, drained but would not spin, filled with water for rinse cycle, drained but would not spin. I have checked the door latch, and have also checked the drawer for soad dispenser, both seem fine. I have read other scenarios and the thought of spending $500- $600 makes me a little sick. Any help and all help would be appreciated.