Your working AND non-working dehumidifiers (and air conditioning units, mini-refrigerators, wine coolers, etc.) typically contain a refrigerant commonly called Freon. Freon is a liquid or gaseous Chlorofluorocarbon (CFC) or Hydrochlorofluorocarbon (HCFC) that is used as a refrigerant.  Since the late 1970s, the use of CFCs has been heavily regulated because of their destructive effects on the ozone layer. This is why dehumidifiers and other devices containing Freon/refrigerants are not allowed to be disposed of in the trash and are not accepted at SWALCO collection events. 
Here's the environmental spiel provided by the EPA Stratospheric Protection section. EPA regulations (40 CFR Part 82, Subpart F) under Section 608 of the Clean Air Act include requirements for the safe disposal of refrigeration and air-conditioning equipment. These requirements are designed to minimize refrigerant emissions when these appliances are managed.
Single Dehumidifier
The good news is that most scrap yards accept and provide safe disposal of items containing refrigerant. A list of local scrap yards can be found under our  "Where do I recycle this?" directory.
EPA - Safe Disposal Brochure