Let's try a standalone Apple Mobile Device Support install. It still might not install, but fingers crossed any error messages will give us a better idea of the underlying cause of why it's not installing under normal conditions.
Download and save a copy of the iTunesSetup.exe (or iTunes64setup.exe) installer file to your hard drive:
http://www.apple.com/itunes/download/
Download and install the free trial version of WinRAR suitable for your PC (there's a 32-bit Windows version and a 64-bit Windows version):
http://www.rarlab.com/download.htm
Right-click the iTunesSetup.exe (or iTunes64setup.exe), and select "Extract to iTunesSetup" (or "Extract to iTunes64Setup"). WinRAR will expand the contents of the file into a folder called "iTunesSetup" (or "iTunes64Setup").
Go into the folder and doubleclick the AppleMobileDeviceSupport.msi (or AppleMobileDeviceSupport64.msi) to do a standalone AMDS install.
(If it offers you the choice to remove or repair, choose "Remove", and if the uninstall goes through successfully, see if you can reinstall by doubleclicking the AppleMobileDeviceSupport.msi or AppleMobileDeviceSupport64.msi again.)
Does it install (or uninstall and then reinstall) properly for you? If so, does your device connect without that message now?