Windows or Mac?
Download the Adobe Flash Player installer(s) directly by right clicking one (or both) of the following links and selecting "Save Target as" (using IE) or "Save Link as"(using other browsers).
If you use other browsers I recommend downloading BOTH - Save them to your downloads folder and DO NOT run them yet.
Close your browser and check the Task Manager to be sure it's closed completely.
Reboot your system.
BEFORE you open anything else, locate and run the installers. Your Flash Player should be updated for IE and other browsers.
If you still have troubles with IE, see: Enabling Flash Player in Internet Explorer
Note: If you still receive a "administrator" requirement error, create a new account (admin) and try it under that account. If it works, you've got problems with your user account. If it doesn't, there maybe some system problems.