You didn't say this in your post, but, have the system's autoplay settings been modified? (Control Panel, Auto Play.)

On my computer, the iPhone gets its own entry in that screen, see the attached screen shot. Is that set to something good, like "open folder to view files"?

Other things to think about:

When I first plug my iPhone into a computer, it prompts me to "trust this computer". Has the user said "No" to that question?

Have the necessary drivers and/or iTunes been reinstalled on this computer? I know that iTunes installs things like "apple mobile device service" and "itunes helper" applications. Sometimes I remove those to keep the system lightweight. Did that get done to this computer?

When plugging in the iPhone, does it show up as a Little Yellow Boo Boo Icon in the device manager?