I got the following to work:
1- Permissions must be set manually on
C:\Windows\System32\Macromed\Flash ( as Administrator -- right click on folder's name then launch Properties, switch SECURITY section and select your user. REMEMBER: your account must be administrator rights. check under Allow boxes there, then Apply all changes)
2- Same process must be done also for C:\Windows\SysWOW64\Macromed\Flash
3- Download latest http://www.adobe.com/products/flashplayer/distribution3.html
4- Use MSI Installer do not use install EXE versions. It doesn’t work. MSI installer worked for me...
I used the standalone uninstaller then the method a2zbus described above and it worked for me. I was signed into my PC as a local administrator so I already had full rights to both of the Macromed\Flash folders. I had also gone through the process in the video linked by Mike M beforehand and deleted various files so that may have contributed to the success as well.
I have a feeling though, just using the MSI installer instead is what did the trick for me. I verified installation by using the "Check now" button on this page: Flash Player Help.