Also, when I took a look at the impeller, I found a long rubber seal that was just hanging out; I am not sure where it came from, or how to put it back. I'm worried that running the dishwasher without the seal will just cause additional problems, so any ideas of where it goes would be appreciated.
The dishwasher is quite old so calling out a plumber here (she's in Germany) probably won't be worth it given the call-out fees alone.
Seal:
(Moderators note) Moved from plumbing