Kenmore 80 series washer will not fill up with out holding down the water reset switch

SOURCE: Kenmore 80s Series Leaks Water into the Bin

Replace the water inlet valve. 285805

SOURCE: Kenmore 80 series won't spin

If it agitates and drains. leaving your clothes clean but soaking wet. It is most likely the transmission/gearbox. the motor is working otherwise it would not agitate. it is stuck in agitate mode and cannot "shift" into spin mode. new transmission will cost 140-170 and takes 2 or so hours to replace depending on skill level. total repair cost parts+labor $300ish you may want to ante up for a new machine at this point. if you cant to the labor yourself.
part# should be this: tho double check using your own model#
Part # AP3096209

SOURCE: Kenmore 80 Series Top Load Washer not agitating

Check out this you tube. Had the same problem today. Tipped washer on its side and replaced coupler between motor and gearbox. Parts are about $15
This is a good diagnosis video.
http://www.youtube.com/watch?v=VYOP0_KCYT0

SOURCE: Kenmore series 70 washer will only fill with water.

I recently had this problem. It was found that the main drive belt broke and the washer would fill but not spin, agitate or drain. I replaced the belt and everything worked again. A defective or disconnected cover switch would also cause the same problem.

SOURCE: Kenmore 80 Series- Washer does not fill up with

Check if the volume of water supplied to the washer from the water line through the hoses attached to it is good. If yes, the screen inside the water-inlet valve if it is clean. If clean, the water inlet valve is defective and you need to replace it. The water inlet valve is located inside the washer on the upper back portion. It is where the water supply hoses are attached to.