you may have sent 240 volts through your dishwasher. if your dishwasher and disposal are on separate circuits, they are probably sharing a neutral (that's how most kitchens are wired). if the neutral gets interrupted trying to get back to ground (like coming loose at the panel) then you actually have one 120 volt phase going through the dishwasher and one 120 volt phase going through your disposal and the neutral, rather than running back to ground, just runs those two phases together. so as soon as you turn on the switch for the disposal, you complete that circuit and send 240 volts through both appliances.
not that this helps you get your dishwasher going, just nice to know why something broke