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Definitely do not use Muriatic acid. The only product that I have ever seen which works is a product call Dishwasher Magic which you can pick up at Lowes or order on line. If the baked on residue is removable, then Dishwasher Magic will remove it.
As for the reason the pump just starts turning on, that is because the small filter board under the bottom drawer in the back of your dishwasher thinks it's detecting water in your base pan below the bottom drawer. If there is no water, then replace this board because the humidity in your area is triggering the board when it shouldn't.
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If you haven't tried Dishwasher Magic, then that why it hasn't worked. If you have tried Dishwasher Magic, then nothing will work.