As a start, generally there is a large area in the bottom of the dishwasher that is removable, and there are some screens and stuff that are cleanable.
In the pic. There's the obvious piece. But that 18" diameter circle is removable. And the ligher grey tube is removeable. Generally all without tools, just snap in / out.
If you take them out you'll at least find a ton a nasty crap. Apparently cleaning this is considered a regular maintenence task. I discovered this at 24. Becuase my family literally never did this growing up.
Anyways, I'd at least do some basic exploring and cleaning before you try the plumber.