I have both a DN2820FYKH and D34010WYKH connected to a TV via HDMI. Both are running fedora 20. They run 24hrs and I have set it up so that they auto-restart during the night. However I have found that if you restart or boot either box up while the TV screen is turned off, the NUCs will not output a video signal. You need to hold down the power button and restart the boxes (while the TV is on) before they output a signal.
Have I missed a setting in the bios or something?