Kenmore Series 80 fills with water and won't stop filling until manually advancing the timer, does not agitate but will spin and drain.

Good day,
Sounds as if the water level switch is bad, or the hose to it has broken, come off or is plugged up at the base where it enters the tub.
Remove the 2 screws that hold the console in place. They are either at both ends front, both ends front but hidden by end caps that have to be un clipped, or lastly at the bottom back.
Pull slightly forward and rotate the console up from the front and away from you.
You will see the water level switch with a plastic hose pressed onto it. Remove the hose, and blow into it with the tube partially filled. You should hear it gurgle. If broken, the air will just escape, if plugged and you cannot get air thru it, it will have to be cleaned.
If everything checks O.K. with the hose, then the fill control (pressure switch) is bad, and needs replaced.

The agitation mode works thru the pressure switch, but the switch is bypassed in the pump out spin mode. That's why it performs as you described.

I had this same problem BUT I figured out why. If I do not let the spin cycle complete, it will do this but if it completes there is no problem. This was driving me crazy because I would let the washer run overnight and didn't realize the water was just running down the drain.