I am sorry to hear that have had issues with the NUC DN2820FYKH.
At this point, I recommend resetting BIOS configuration to see if there is something wrong with boot process detecting video signal.
Please make sure you keep using HDMI to HDMI cable, this is recommended by Intel.
Take a look at this link for information about how to reset BIOS on your computer:
https://communities.intel.com/message/232498#232498
Allan.