I would suggest that you temporarily connect your NUC to a different monitor (or TV) to see if the issue is specific to the HDMI output. When powering on, holding the power button for 3 full seconds will cause a (text-based) boot/recovery menu to appear. This may make it easier to check. Note that, if you hold the power button down for too long (i.e. a full 4 seconds), the hard power off feature will be invoked and let you know you've held it too long...
P.S. You'll get more NUC-related eyes looking at your posting if you place it in the Intel NUC support forum. This forum is for the older Intel Desktop Board products.