I had the same issue with my iPhone 4, iOS 7.1.2 (I know, it's old), after downloading and overwriting the iTunes 12.3.0.44 update to my Lenovo Windows 10 machine via the iTunes Update window.
After the update, when iTunes no longer recognized my iPhone, I called Apple Support, fully prepared to pay the $29 support fee. However, the Apple Genius graciously told me that I should have removed the earlier version of iTunes from my computer first, before installing the update (why wasn't that included in the update notice ?).
Of course, there is a very specific uninstall process for iTunes. Uninstalling the iTunes software in any other order than the following may cause problems...
1st - iTunes
2nd - Apple Software Update
3rd - Apple Mobile Device Support
4th - Bonjour
5th - Apple Application Support (both 32 bit & 64 bit)
Once I uninstalled the earlier version of iTunes, I downloaded the new version and installed it successfully.
My iPhone 4 was subsequently recognized immediately.
Problem solved !!