I am having a very similar problem with my
GLTF2940FS1. For a while now, it would sometimes not run, but ignorning it for half an hour then running it would fix the issue. And sometimes when it did run, it would not have rinsed/drained... just my laundry sitting there wet.
Not it won't run at all. Running it causes the door to lock, some sort of an electronic hum for ~5 seconds, and then the door would unlock. Diagnostics gives an E6E with 6 beeps. I cleaned the filter first just to be sure, but the problem is still occuring.
Ordering a replacement main control board to see what happens. For those who are following in my footsteps, to get to the main control board you need to remove the two screws at the top back and slide off the top panel. To fully get to the unit, you will also have to remove three screws you see when you remove the dispenser tray, and a couple screws you will see when you remove the top panel.