I have a kenmore 720 series fairly old and it won't spin automatically to drain water?

You said it won't spin automatically... will it spin if you advance the timer manually? Does the spin cycle work on another setting i.e. gentle setting, perm. Press? It could be several things, try adjusting the load so that the load is evenly balanced around the tub, even the slightest difference can cause a no spin. Another tip, make sure the legs are evenly adjusted so that the machine is level. Those are the simple solutions... It could also be that the timer needs replaced, not a terrible problem to resolve but start with simplest first.

I was surprised to see no response on this one. So I hope this helps.