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Run an empty load and add a cup of white vinegar.

Clean out the filter(s) and consider running a clean cycle. I bought a heavily used portable unit a few years ago and lemi-shine did a great job. I've had good results with affresh in other appliances. I really don't think brand matters too much, the cleaning solution is pretty basic.

Usually they drain into the garbage disposal if preinstalled, so if your sink works the dishwasher is probably fine.

Often time they share an outflow with the kitchen sink, so the plumbing may not be as backed up as you imagine provided that you use the sink regularly. That said, proceed with caution.