No matter which wash setting I choose, the washer starts filling but drains before it gets a couple of inches of water in the tub. Since it will never get full, the timer never advances (no matter which of the four wash settings I start). I'm assuming it isn't the timer (I guess it can't advance if the first part of the cycle never gets done), but what else should I check? I have no appliance repair experience, but I'm willing to try (since I'd rather not buy a new washer). Thank you!

Thank you, Eric! It goes into a standpipe in the wall. It has been there for over 4 years, and never had this problem. Could it be the standpipe is blocked?

Gosh, I feel like an idiot! I pulled on the drain hose, and it did appear to be sealed. I heard a sucking sound, and then some water from the hose drained down the house drain. It was definitely siphoning. I'm so glad you answered my question on this forum! You saved me a service call :) Thank you again!