+1 Especially when it's not known what's wrong. Could be a plugged up drain hose.
That's my vote.
From the description it sounds like the first place to look would be a clogged drain hose between the DW and the disposal. Could also be clogged at the pump inlet. On my Kitchenaid, you can easily remove the lower arm, then the screen underneath and get to the pump intake. If it were mine, that's where I'd start, because it's easier than checking out the hose. On mine, you can turn the arm backwards while lifting up and it comes right off. But how the OP's comes apart, IDK. You can pull up parts diagrams at the online appliance parts stores that show how it's put together. That is often enough to figure out how it comes apart.