I passed by the Wascherei you mean today, on Eisenbahnweg, near the steps next to Coop City. It isn't a Laundramat, as in self-service, but they dry clean, wash, and/or iron your clothes for you, I think it said it takes two days.
As I said, there are no self service laundromats in Baden. The dry cleaners (such as Jet) also provide washing services.
There are laundromats in Zurich. There have been threads on this (as posted above) which can be found if one does a search. Some of the locations may not exist anymore.
According to the yellow Pages the nearest one to Baden is in Zurich on this street; Limmattalstrasse. Not very useful if you just want to do a quick wash!