I had the exact same problem! I tried on a few computers that I KNOW worked in the past. I don't know why this worked, but it did:
1) Checked that Apple USB driver was installed (it was)
2) Restarted the phone.
3) Plugged the phone into a USB port I knew had worked.
4) Navigated to Devices and Printers, and saw in the "Unknown" category, a generic Apple iPhone.
5) Right-clicked and chose Properties. I then also tried Troubleshoot (it didn't find anything). Note also you can navigate to the file structure on the phone, so worst case you could always get them that way.
6) Unplugged, and then replugged the USB into the phone. Voila.
Again I don't know why, but I suspect I had to help win7 find the ios 10 phone (it's a 5s).