Try using Revo Uninstaller. Even if it can't uninstall the application normally, it will force it to uninstall by wiping out all traces of its presence from the system.
After that, navigate to Adobe Downloads page, press the yellow Install now button, save the file to your computer and install the program following the provided instructions. If you still have issues opening the PDF files, I suggest you try Foxit Reader, Nuance PDF Reader, or SumatraPDF.