Kenmore washer spin cycle drains but doesn't rotate
I fix my own stuff, but don't know about your washer. However, a quick search revealed this to be a common problem &amp; I ran across an old blog that matched your symptoms perfectly. Kenmore washer won't spin out all water from clothes.

Although, the parts involved in resolving the multiple problems, appear to total more than $300 for the parts alone. You can call a local Appliance Repairer for their estimate for the typical course of action for this common problem. But, based on just parts cost I'd suggest getting a new washer with a new warranty.