Says Flash installed but is not

Question

Flash player says it has successfully installled, but it hasn't.  See lots of other similar threads, but none of the suggestions seem to help, and our computer is not identical to any of the threads I've found. 
We have two browsers - Mozilla Firefox and Internet Explorer.  Mozilla Firefox works fine, no problems at all (first time). 
I have tried installing on Internet Explorer multiple times, over multiple weeks, and just tried again I think three times tonight.
I changed IE to default browser (weeks ago). 
I have changed settings to medium internet security and ensured scripting was enabled (which it was already, but was previously on medium high security). 
Goes through initialising etc, no error messages at any point, says installation successful and you are now running Flash.
It does not come up with the agreeing to license dialogue box, or where it should say do you want automatic updates. 
If try to use on any site, comes up with needing to download latest version of Flash. 
If I go into Flash help sections, comes up as blank box under what version is installed. 
If I go to Flash can you see the movie it also comes up with a blank box. 
It does show Flash IS enabled, version 11.8.800.94 
Internet Explorer we are using is Internet Explorer 10. 
Is a laptop, has a 32 bit system. 
OS is Windows 7. 
Any ideas how I can get Flash to install (not just say it is installed, but actually installed and working), without having manual work around of copy and paste the web path to our Mozilla Firefox browser (pain because I primarily use IE because I like shortcut setup). 
Thanks heaps for any help you might be able to give.
Liana

Answer 1

Hi Pat
Thank you for responding.  Now working - thank you.  Details below.
Tried to download using “Direct Links For Internet Explorer” on the link provided.  I got to click the tick box “I have read and agree to the terms of the Flash Player License Agreement” and press install.  (This did not come up previously, but did have downloading progress bar and Flash notification of installation successful previously.)
It then immediately came up with “the installer will automatically continue when these conflicting applications are closed: Internet Explorer.” I shut down IE, and waited 20 minutes, nothing appeared to be happening.  I closed box (with cross in upper right hand corner, not pressing “quit”).  No further dialogue boxes, no messages, no errors, but no successful installation either. 
Redid and closed IE (and all other open programs) at point of agreeing to terms of Flash coming up and before clicking agree and install.  Came up with same dialogue box “the installer will automatically continue when these conflicting applications are closed: Internet Explorer”, even though Explorer was then closed.  I waited 20 minutes again, again no further messages or anything else from Adobe, again closed with cross, again no further messages or anything else from Adobe.
Redid using “Flash player for Active X (Internet Explorer)” also on page you gave link to.  Did exactly the same as above.
Tried using and still no success.
Flash player was already enabled.
Active X filtering is a bit different on my explorer (IE10) – has single entry for active X, which just has a tick, viewable when just drop down the main Tools toolbar.  I unchecked, and, hey presto, Flash works.  I tick, and get message saying need to install, re-tick, refresh, and Flash works.
Thank you.  Now just not sure if I should just take Active X filtering off all the time or not.  Presumably it is to stop nasties, anyone know what the risk is?  In the mean time, I'll just un-tick it when I need to use Flash.
Thanks again
Liana