I know this post is pretty old, but I thought I'd post my answer in case someone runs across it like I did.
This issue was definitely caused by the water level pressure switch. Here is what I did to fix it.
First, I checked to water tube attached to it to make sure it wasn't plugged and wasn't full of water. It was fine and I could easily blow through the tube, so it was fine.
I then took the switch out - Watch this video for how to do that. (https://www.youtube.com/watch?v=oi8uUPFgxbI
Once I had the switch out, I decided to see if it could be repaired, instead of having to buy a new one - So, I took it apart.
The end where the hose plugs in is pretty much a cap, and all around the cap are clips that keep it in place. Popping each clip with a small flat head screw driver, I could then pop it off. Underneath was a rubber diaphragm with a plastic center piece. Remove the diaphragm and you'll see the inner workings of the switch. It's a pretty simple switch. In the center, you'll see a white plastic piece that connects to a metal arm, that opens or closes the circuit. There are 3 latch tabs around the switch holding the guts of the switch into the housing. Push out those 3 tabs and you can pull the inside of the switch out. Once the switch is free from the housing, you'll see a column with an end plastic end piece on it. If can pop off that end piece and you will see 2 springs inside. For me, those springs were old and just not providing enough tension to keep the circuit open, so I took out the springs and stretched them out some. This provided more required tension to compress the springs, so that that diaphragm couldn't push down the center rod as easy. Once I stretched out the springs a bit, I put the switch back together (Be careful to see how it goes together, as the plastic end cap and the center rod fit together a certain way. Also, placing the end piece with the hose attachment back on with the diaphragm in place is a little tricky.)
I installed the switch back into the control faceplate, hooked up the wires and the water level tube, and tested. I had a working washing machine again!!! I know the above SEEMS like a lot, but the whole process took MAYBE 25 minutes. If you're careful in disassembling and reassembling the switch get it working pretty quick, and free!