Keeps filling with water, but draining at the same time!

Try eserviceinfo.com/index as per your 80 series. There are various downloads there that may help access the water level sensor which is most likely the problem.

Not sure if you have already done this, but is the drain hose higher than the washer?

Has your drain for your washer backed up recently? Or is the drain hose from the washer sealed into the drain pipe, meaning that you can't just lift the hose out anymore? There needs to be air around the drain hose or it will cause the washer to allow water to be siphened threw the drain by not closing the filling valve. This can also happen if your drain is backed up. Rooter the drain out and make sure that the drain hose is not sealed up to the drain pipe and see if that fixes your problem.

Possibly your problem is the tube that tells the machine when the water is full. It may be blocked.

I had the same problem too on one of my washers (not kenmore) it didn't complete cycle because someone turned off the hot water valve. soo i turned on the hot water and it worked fine. keep in mind that mine wasn't a kenmore. hope this helps some...

Check the following before replacing the timer.

1. Clogged drain line or water pump
Check to see if there's something stuck inside the pump or the drain hose connected to the pump (pump is usually located at the bottom and towards the back of the washing machine).

2. Water Pump
If the drain line isn't clogged, you may have a problem with the water pump such as a frozen pulley or a broken impeller. If that's the case replace the water pump. Note: if you have a belt driven washer, check the belt(s) for cracks, as this would be a perfect time to replace the belt(s) if needed.

POST ME THE MODEL NUMBER. AND ALWAYS POST MODEL NUMBERS WHEN NEEDING ASSISTANCE PLEASE:)))

Almost went and bought a switch until I widened by search for "kenmore washer 80 series overflow" and came up with this:
http://www.fixya.com/support/t1206464-kenmore_80_series_overflow

Turns out that a couple weeks ago, I had a really unbalanced load that probably shook off the tubing. Anyhow, saved me a trip to the supply store AND cost. Thanks to the original poster!

You have a siphon condition. The water is siphoning out as it fills.
Make sure you only have about 6 inches of the drain hose stuck into the house drain and make sure there is an air gap where the hose goes into the pipe so air can get into pipe. If you have the drain sealed to keep water from backing out of it, you will need to get the pipes cleaned for the washer to work properly.
The pressure of the water going through the pump during siphon is not enough to turn it on the machine.
Post back if you need more help.