In my Windows 7 environment, removing and reinstalling following the instructions of turingtest2 didn't quite work for me but one extra step did.
Near the end of the reinstallation, you will be asked to "Finish" the installation. DO NOT CLICK FINISH.
Rather, connect your Apple device (iPhone, iPad, etc.) to your computer. This will trigger your PC to install drivers for your device (you'll see the notification on the lower right). Windows will automatically search for the correct drivers ("obtain device driver software fr4om Windows update")--this can take a few minutes--and then notify you when the device is ready to use.
Once you get this notification, then you may click to "Finish" the iTunes (etc.) installation. In my case, it finished and iTunes opened as it should.
Apparently, connecting the device before finishing the iTunes installation forces the installation of the missing files.