It sounds like you're running into an issue with Internet Explorer 9. If you're on a work computer, or you don't have Administrator access, you may lack permissions to enable plug-ins; however, it sounds like this can also happen if your Windows user profile gets corrupted.
I found the following thread on the Microsoft forums. The correct answer is at the bottom of the thread:
http://answers.microsoft.com/en-us/ie/forum/ie9-windows_7/cannot-enabl e-addons-as-the-feature-is-greyed-out/6028edfa-c864-48b0-aa24-e08afb5e a831
Short of that, you might consider just running Chrome, which ships a built-in Flash Player:
https://www.google.com/intl/en/chrome/browser/
