Donna,
You have both versions of Internet Explorer installed if you are indeed using the 64bit version of the OS.
The easiest way to see which one is running is to open the Task Manager and look for iexplorer in the processes, after its running of course. The 32 bit version will have *32 after it stating its 32 bit. 64 bit will be plain.
Find the 32 bit version and run it in lieu of the 64bit version. Go to the adobe page and see if the plug in is installed. Note the rotating flash picture may rotate and state that version 9 has been installed but if you go else where such as this page
Speedtest.net - The Global Broadband Speed Test
and find most of the middle of the page missing it has installed incorrectly.
Go back to adobe and find the application that removes Flash. Yes they do have one. Restart your system once removed (to be safe) and then go back to Adobe and reinstall it (hopefully this time correctly). Ensure you are using the 32bit version of IE. Go back to the speed test site to confirm correct installation.
Hope this helps. Yep - been there done that