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The problem is new for me; could you give me more details of your NUC configuration. Let me know the current NUC model, current BIOS version, BIOS settings (is it as default).
Please tell me if F10 option allows you to boot.
So you manually upgraded the Linux kernel to what version? Per default 16.04 LTS does have kernel 4.4 and if you're not an enthusiast or experiencing any problems, you should stay on that kernel version.
How to fix your problem:
On bootup you should see the GRUB bootloader and be able to boot Ubuntu with the old 4.4 kernel, simply by choosing it with the arrow keys. When you're back in the OS, uninstall the new kernel and you should be fine