I found the solution for my problem. It seems to be a problem with the female connector on the iPhone 4S itself. I discovered this by accident: I dropped it while it was plugged in to the Windows 8 machine, and for the very first time, I heard that water-splash sound indicating that the computer recognized a new device. Then it immediately made the disconnect sound. I picked it up, unplugged and replugged several times without success. But when I applied downward pressure on the connection at the iPhone, it finally became recognized. For the first time, Apple's USB driver was loaded up. I cannot explain why I never had this problem when plugging it into the Windows 7 machine, bad connector or not, even when going back and forth between the two machines as I described in previous posts. However, the fact that I never had a problem connecting my iPod to Windows 8, which has the new iPhone5-style connector, was a good clue.
I had both Apple and Microsoft technical support technicians look into my computer, and both swore that everything looked perfectly normal as far as the iTunes software and the Windows 8 OS was concerned. They were right! (By the way, although technical support is not cheap, these folks were very informative, helpful, and tenacious).
Bottom line is that if you have USB connection issues with your iPhone 4, here is another thing to try: firmly jiggle the connector to make sure it's in tight, then apply steady upward or downward pressure on your connection at the iPhone 4S. That just might do the trick.
Good luck!