Try using the full installer from http://helpx.adobe.com/flash-player/kb/installation-problems-flash-player-windows.html#mai n-pars_header
If you still have problems, please post the contents of the FlashInstall.log file from C:\Windows\system32\Macromed\Flash
I tried using the link you gave me. I, again got the message "user has insignificant privileges". However, I was able to play games which required updated flashplayer, and when I check flashplayer via the Control panel, I found that the plug in version was miraculously updated. I should mention that I am using windows XP on a 7 year old computer. I think it may be pre-senile. I am trying to keep it going long enough that they get any bugs out of windows 8, and then I think its time to upgrade.