Adobe flash player not working

+I installed Adobe Flash player into my mac mini and for some reason it only shows the installer.+

I believe the Adobe Flash installer installs flash capability into your web browsers, such as Safari or Firefox.

AFAIK, you don't actually end up with a stand-alone application. You access flash content through the web browser.

What web browser are you using?

Did you follow the instructions to be sure to quit your web browsers before installing Flash?

Safari.
+Yes, I closed all browsers.+

By "closed" I hope you meant quit. Closing the windows, still leaves the browser running.

Is it a particular site's flash video you can't play, or do you have problems with all sites, for example youtube.com as well?

Did you run an installer, or just unzip a plugin file to some location on your system? The plugin should be in the internet plugins folder, so if you got a zip file package of the plugin and just extracted it without directing the file to be placed in the appropriate folder, the browsers will not find it and use it.

The simplest way to be sure the browsers shut down and are allowed to load the plugin correctly is to restart the whole system. Your browser(s) will detect and load it upon the next launch after the restart.