None of my Apple devices would connect to iTunes on my Windows PC. Apple help on the PC and the official Apple help sites on the web were also of no use. This site, however, had the solution to my problem, which was to install the Apple USB driver.
As it suggested, my Apple device was improperly located under Mobile Devices in the Windows Device Manager. It should be been under the USB list. I followed the instructions and it worked.
I did later find it in an Apple discussion here