I have Windows 7 Home premium. I downloaded the installer, tried to run it with no results. No window opens up, no response. I clicked on the installer again. A window opens up saying "Only one instance of this program may be run at a time." I then start Task Manger. In the Applications tab, there is no instance of Adobe Flash Installer running, however in Processes tab, the installer is there. I have a feeling the installer is hanging up somewhere
My recommendation would to be to reboot the machine, then try the installation before launching anything else.
If that doesn't work, try the offline installer using the direct download links at the bottom of this page: