🙂 Good-O.
Working on the principle that this might be caused by some subtle damage to the QuickTime program files relating to ActiveX controls, I think we should try a clean uninstall/reinstall of QuickTime, taking a few other explicit precautions along the way (just in case).
First, download and save a fresh copy of the QuickTime installer from the Apple Website. (Don't run the install on line, and don't start the install just yet. Get the installer that
doesn't mention iTunes.)
http://www.apple.com/quicktime/download/
Now head into your Uninstall a program control panel. Uninstall QuickTime.
Next we'll clear away any leftover program files and folders.
In "Computer" open "Local Disk C:" or whichever drive you have your *program files* installed on.
Open the "Program Files (x86)" folder.
Right-click on the "QuickTime" folder (if it still exists) and select "Delete").
Go back into "Local Disk C:" or whichever drive you have your *operating system* installed on.
Open the "Windows" folder.
Open the "SysWOW64" folder.
Right-click on the QuickTime.qts and QuickTimeVR.qtx files (if they still exist) and select "Delete".
Restart the PC.
After the PC restarts, do not open any applications (especially not either of the IE 8 browsers). Disconnect from your network and/or the internet. Now switch off
all your security software. (Firewall, antivirus, antispyware.)
Now start the QuickTime reinstall by doubleclicking the QuickTimeInstaller.exe file you downloaded earlier.
(This may also update your Apple Application Support to version 1.3.0 ... I'm not sure whether or not the QT 7.6.6 installer bundle has been modified to include the new version yet.)
Reenable all security software prior to reconnecting to your network and/or the internet.
Did the QuickTime install seem to go through okay?
If so, fire up the 64-bit version of IE 8 and browse to a website containg QuickTime content ... like Apple.com, for example. Do you get asked by IE to install the ActiveX component this time around? If so, does it install properly this time?