What driver packages have you downloaded and installed from Intel's Download Center? Don't trust Intel's Driver Update Utility (it's a complete POS) and especially don't trust Windows 10 to give you the right drivers. The download page for your NUC is here: Downloads for Intel® NUC Kit NUC6i5SYH. Download and manually install all of the latest packages that are for your version of Windows 10.
1. I'm assuming from your post that you are using Logitech wireless keyboard and mouse. Looks that they are not recognized in the Windows. As a starting point set your bios to default setting:
- press F2 during boot to enter bios settings
- press F9 to set bios to default settings
- press F10 to save the settings and to exit to Windows.
2. Download Logitech Unifying Software and install it: Unifying Software - Logitech Support
3. Run the Logitech Unifying Software from Windows start menu.
5. Press next.
6. Follow the on screen instruction (switch the on-off switch on your mouse first to OFF than to ON) to pair your mouse to the receiver.
7. Once your mouse is detected you will see confirmation notice - select Yes and than Next to continue.
8. Select Pair Another Device and repeat para. 6 for your keyboard.
9. Once your keyboard is detected, select Next and than Finish.
Thank you for joining the thread.
For us to further assist you and to help you with the specific problem, please create a new thread, make sure to add all the details in regard to your system. This way the next agent will have a better look at your specific scenario, you can add this thread as a reference but I recommend creating a new thread in order to isolate your case.