Just ran in to this same problem with my GE washer. Please tell me if I have diagnosed this correctly.
I did the "Field Mode Test" and no error LED's lit in positions 2, 3, or 4. Would not agitate in either 7 (AL) or 8 (AH) positions and would not spin in the 10 (PS) position as well. Otherwise, everything checked out. Next I went to the motor inverter board status indicator light. I got a normal .5 second on/off flash when it should be running.
So, I believe that to mean the motor is dead, correct?