Recently I have got a problem. My NUC7 refused to boot OS. The sympthom was exact as in this posting. The power button turned to solid amber/orange color (no blinking).
I've tried holding the power button for any length between 3 to 15 seconds, no changes.
Fortunately I solved the problem following an advice from Intel NUC community. The link to possible solutions is here.
I diassembled the NUC7 to reach an opposite side of the main board (with cooling fan and CMOS battery). I disconnected the battery for 15 minutes, and then connected it again. It solved the problem with power indicator and booting.
Was sure my NUC was dead and the battery trick revived it. I owe you a glass of your favorite drink.