Okay. Rather than letting the installer do the expansion, we'll expand the installer ourselves.
Download and save a fresh copy of the QuickTimeInstaller.exe (installer) file to your desktop.
Download and install the free trial version of WinRAR:
http://www.rarlab.com/
Right-click the QuickTimeInstaller.exe and select "Extract to QuickTimeInstaller\". WinRAR will expand the contents of the file into a folder called "QuickTimeInstaller".
Open that folder and doubleclick on the QuickTime.msi.
Does that install go through?