Paul's Answer:
Hi Gregory
I have had a lot of problems with these ADP and ADG type dishwashers the fill chamber on the side of the machine can clog restricting the flow of water in and the the machine times out, also the water valve can fail but not that often. the main thing is that if the flow jug that is built into the fill chamber does not register water coming in then the dishwasher will time out. if you take the side off then watch it when it tries to fill. i have put a link to your Whirlpool ADP4305 fill chamber below and you will see it comes with impeller jug.
To assist you with this with repair on your Whirlpool dishwasher i have put videos below but they might be on other makes but the principle is the same.

Fill chamber with impeller jug to fit all these models:
ADG332IX, ADG332SAV, ADG332SWH, ADG3440AV, ADG3440WH, ADG3540AV, ADG3552IX, ADG3552WH, ADG3962IX, ADG4340, ADG4952M, ADG6230/1IX, ADG6230IX, ADG6320IX, ADG6340/1AV, ADG6340/1IX, ADG6340/1NB, ADG6340/1WH, ADG6340/2IX, ADG6340/2NB, ADG6340AV, ADG6340IX, ADG6340WH, ADG642/1BR, ADG642/1IX, ADG642/1WH, ADG6441WH, ADG644BR, ADG644IX, ADG644NB, ADG644WH, ADG6552IX, ADG6552WH, ADG6560/1WH, ADG6560IX, ADG6560WH, ADG6561IX, ADG6565IX, ADG6915IX, ADG6916IX, ADG6962IX, ADG7190, ADG7195, ADG722AV, ADG722WH, ADG7340, ADG7440, ADG7441, ADG7450, ADG7460, ADG7461, ADG7540, ADG7540/1, ADG7550, ADG7560, ADG7560/1, ADG7680, ADG7780, ADG7790, ADG7952, ADG7960, ADG8100, ADG8200, ADG8441/2IX, ADG8441/2NB, ADG934/1AV, ADG934/1WH, ADG9340NB, ADG9340WH, ADG934AV, ADG934IX, ADG934NB, ADG934WH, ADG937/1S, ADG937/S, ADG944AV, ADG944IX, ADG944WH, ADG9540/1AV, ADG9540/1WH, ADG9540AV, ADG9540NB, ADG9540WH, ADG957/3M, ADG957M, ADG975AVM, ADG975NBM, ADG975WHM, ADG977/3, ADG993/1AV, ADG993/1WH, ADG993AV, ADG993WH, ADG994AV, ADG994WH, ADG995AV, ADG995IX, ADG995WH, ADL248IX, ADP241SWH, ADP242SWH, ADP2440AL, ADP2440WH, ADP2540WH, ADP2549WH, ADP2556WHM, ADP2652WH, ADP2756WHM, ADP2962WH, ADP2966WHM, ADP4000WH, ADP4400WH, ADP4403WH, ADP4404/5WH, ADP4407, ADP4440WH, ADP4500/7, ADP4500WH, ADP4501/5WH, ADP4501WH, ADP4502/5/S, ADP4502/5S, ADP4502/AL, ADP4502AL, ADP4504WH, ADP4508, ADP4544WH, ADP4601, ADP4601/1, ADP4601/S, ADP4601IS, ADP4601WH, ADP4602AL, ADP4608, ADP4731/5/S, ADP4731/5WH, ADP4731WH, ADP4732AL, ADP5406, ADP5440AL, ADP5440WH, ADP5540/1AL, ADP5540/1WH, ADP5540AL, ADP5540GR, ADP5540WH, ADP5740WH, ADP5756PLM, ADP5962WH, ADP5966WHM, ADP6406, ADP6736WH, ADP6746WH, ADP6830/5WH, ADP6830WH, ADP6836WH, ADP6940/5IXM, ADP6940/5WHM, ADP6940IXM, ADP6940WH, ADP6946IXM, ADP6946WHM, ADP7406, ADP7406/S, ADP7408, ADP7409IS, ADP7409WH, ADP8000, ADP8000/IX, ADP8000IX, ADP8332, ADP8800, ADP8800IX, ADP8900WH, ADP903/2AL, ADP903/2WH, ADP903AL, ADP903WH, ADP931AV, ADP931WH, ADP941/1WH, ADP9410/2WH, ADP9411/2AL, ADP9411/2WH, ADP941WH, ADP951AV, ADP951WH, ADP952/3WHM, ADP9520/1WH, ADP9520/2WH, ADP952WH, ADP952WHM, ADP961WH, ADP9620/1WH, ADP9620/2WH, ADP9621/1WH, ADP9621/2WH, ADP962WHM, ADP970WH, ADP972/1WHM, ADP972/2WHM, ADP972WHM, G2PDWI/WH, ADP4305,