Hello.
I have a Kenmore Elite Catalyst, model# 110.20052994. About a week ago, it would not drain. I even tried pressing the drain button on the control panel, but it did not work.

So, I drained the water by hand and tried to run through another small load cycle. Now, the washer continues to fill, even overflowing. The only way to stop it is to turn off the washing machine. There is nothing wrong with the drainage hose. Any suggestions?

It sounds like you have a water filler valve problem, with your washer emptied turn the water faucets back on and turn on the washer, if it starts filling turn your timer knob around several times, like you were hunting a cycle you wanted to use. This may make something dislodge from the valve. If not then do the same thing with your water control knob. Turning it from hot to cold and then to hot again... I hope these work... if not and if that is your problem you may need a new water valve. They could be available at Home Depot or some place like it.