Assuming you are in the administrator account, first check Add/Remove Programs to see if you have Adobe or Macromedia Flash installed. If yes uninstall them using the new Uninstaller provided by Adobe and reboot (some computers require a reboot to completely uninstall programs)
http://www.adobe.com/cfusion/knowledgebase/index.cfm?id=tn_14157

Then try to download the Flash player again from the following site:
http://www.adobe.com/shockwave/download/download.cgi?P1_Prod_Version=ShockwaveFlash

However, it has been reported that some people are having issues downloading the full version directly from Adobe. If that is the case, you may want to try to download it as a standalone.
http://www.softwarepatch.com/internet/flash.html

Note: Flash Player is not a program per se. It is a plug-in to your web browser to allow flash content to be displayed and is required for many gaming sites.
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Afterwards check your setting in IE. Go to Tools, Internet Options, Advanced and scroll down to the Multimedia section and ensure that the appropriate settings are indicated.