The big issue with iTunes was NOT with Win 10. It was Win XP. At a certain point in time, you could not run the latest version of iTunes with WinXP. That led to problems. I'm still running the same iPhone 5 (not 5S or SE -- the original iPhone 5). But I needed the latest (at the time) version of IOS but to run that, I needed the latest iTunes but they had capped off the version of iTunes I could run with XP. I broke down and got a new PC with Win 10 (upgraded to Win 10 Professional). Now I have the latest iTunes and running on the latest (patch-wise) version of Win 10 Professional. The last version of IOS that I can run on my iPhone is 10.3.3 and it all works fine. No issues with Win 10 at all.
Suggestions?
Here are a few of mine:
1) Verify that you can logon to all of Apple's websites with the proper credentials. This includes iCloud (www.icloud.com) and Apple's main sites. I also believe that there is a website for iTunes (www.itunes.com). Make sure all of these work well.
2) Make sure you are on the latest patch level of Win 10. If you stopped a Win 10 update while it is in progress, something can easily be wrong with your Win 10 installation. Never kill an update in ANYTHING once it starts, even if most things appear to work. There are plenty of Windows DLLs and other configuration files that need to all match.
3) Make sure your iTunes is the latest and installs cleanly. Make sure you can uninstall it using the add/remove programs feature. Never try to uninstall anything by deleting files or folders. All you need is to miss a single file that is sitting under C:\Windows\system or system32 or any sub-folders and you are messed up. The only exception to this is if the manufacturer (in this case, Apple) supplies you with detailed instructions for a manual uninstall. Remember Symantec products? How complicated a manual uninstall was? Miss a registry entry (I'm guessing you deleted all of those when you uninstalled?).
4) Drivers -- These should not be an issue but, I'd go after the PROPER uninstall and verify no Apple drivers exist under the device manager, just to be on the safe side.
5) Another thing to try: in iTunes, go to the "account" menu item and, under "authorizations" DEAUTHORIZE your computer. Then reboot and go back and repeat but this time AUTHORIZE the computer. You should need your Apple user name and password. I heard this fixes a lot of stuff. You may want to deauthorize, reboot, uninstall (properly), check for and remove any drivers, reboot, then reinstall and reauthorize the computer.
Finally, try something different. Use a different Win 10 computer (friend, family, ...) and see if this is an issue with YOUR installation or if this is about YOUR Apple ID that you need to access the Apple store. Check out: https://support.apple.com/itunes for more help or, if this is a laptop, bring it to an Apple store. The guys there are really good. But I hate to mention this. I'm not having the same issue you are having on Win 10 and iTunes and I have not heard of anyone else having an issue (Please, I'm not doubting you but pointing out that this could be local to your computer -- and watch out for the registry! If your database got deleted but the registry still points to an old location.... ).
I hope something in here helps.