About a year ago, the washer was doing a similar thing, where it would shut off before the spin cycle started. The coin trap was completely clogged then, so I checked it first this time. It was clear, so I took the drain pump out and checked that as well. Nothing seemed to be physically wrong with the machine, so I put it in diagnostic mode, which gave me error code 43 when I tried the spin cycle. This one of the codes for a bad control board.
Replacing the board only took about 15 minutes. The hardest part was prying the wire anchors from the old board. I had to jimmy them out with a screwdriver.
The washer works great now!