The wash pump motor should be running while it fills. The water will add resistance to the wash motor impellor which can then be detected by the control board. That is how it knows when there is enough water in it and to stop filling. It should however come up with an error code U1 if it does not detect that the water has primed the pump after 1 minute. Very rare that these motors fail. The start capacitor does fail often so I would try a new capacitor first and see if pump starts. It should not be that hot. That is a sign that it is trying to go but can't. If capacitor does not fix it then either motor or motor control board is faulty. Do you have a multimeter to check the motor windings?
Lincoln Appliance NZ, July 2012
