If I leave the door of the dishwasher closed, whether there are dishes inside or it's empty, it develops a rotten smell. It does this even when I leave the door open after running it to make sure it's completely dry. I've tried the following tips that I've read on the internet, to no avail: running a cycle of vinegar and water; running a cycle of bleach in the detergent cup with the racks removed. Any help with how to get to the drainage lines to clean them (or other ideas!) would be appreciated.
And... Solved
This sounds to me like the drain hose is incorrectly connected to the drain, causing kitchen sink wastewater to back up into the dishwasher.
The dishwasher drain hose sits lower than the sink drain, and this must be accounted for to keep from having a backflow situation. There is a simpler way to do this than my instructions below, and while it may work, any future clogged drains will cause your issue again.
The proper and most sanitary way would be to install an air gap into the sink. This device fits into one of the extra holes on the top of your sink and has a cap (usually chrome) to make it look nice. The air gap device has two connections, one that comes in from the dishwasher and the other that flows back down to the drain. The air gap keeps you from having a direct hose connection between the dishwasher and the drain and will allow for the dishwasher to overflow into the sink if the drain pipe gets clogged.