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.
@leopck how did you disassemble the NUC to get to the battery? I am experiencing the same problem but cannot figure out how to get to the CMOS battery...