I have exactly the same problem. I've shut down the browser and installed from a folder, removed every Adobe, I've done %appdata%Macromedia removals and removed Flash folders and uninstalled and done clean installs and started and restarted and restarted my PC (Windows 7, using Firefox). I've used the 17MB file from adobe and the small application file. It's frustrating because every "help" link circles back to the "did you check to see if Flash is installed on your computer?" baby pages.
In short, I can download and download and Run and Run, and nothing happens. The install window never appears, and although the process can be found in Task Manager, nothing ever happens. If I try to run it again, I get "Only one instance of this application can run," although I can't find it RUNNING anywhere.