However when I reach this screen (shown below), I click install and the window disappears. I've tried many different things I've found online for fixing 'Hanging or Crashing Apps', however I'm not sure if this is the problem. Thanks for any help.
Instead of using the AMD Auto-Detect and Install Tool, try performing a clean installation of the graphics drivers. Download the appropriate drivers for your graphics card directly from the AMD website and follow their installation instructions.