Don't go with the control board on this! It seems like that is what it should be, but in most cases - replacing the wash motor is actually the answer. Especially in the cases where the dishwasher fills, soap dispenser opens, etc...
For whatever reason - Whirlpool did not include any type of motor feedback circuit on these models. The motor has a weak/poor internal connection, and is not running when it is under a load(i.e. - full of water). Because there is no feedback circuit - the control board is still sending the voltage down, and 'thinks' that the wash motor is running. It will go through all of the other cycle functions normally, but you will obviously have dirty dishes at the end of the cycle. These cycles go for 3+ hours too -
The part that I am recommending in this case is called the 'Sump & Motor Assy'. You will also need a complete model number when you find this part! You are missing the final digit in the model number provided. Open the door and look inside at the edge of the tub on the right or left-hand side. The final digit will be a number - 0,1,2,3,4,5, or 6. These are all different versions of the same model, and the part number will vary, depending on the version. Hope this helps -