That remains to be determined...
Power off, remove your RAM SODIMM and power on. You should see the Power LED blink as a result of there being no RAM installed. Power off, reinstall the SODIMM and then power on again. Do you see the Power LED blink this time? If so, it means that there is something wrong with the SODIMM (either it is incompatible or it is faulty).
If the power LED stays on solid instead, this means that the SODIMM is passing initialization. At this point, you need to look at the state of the BIOS. I suggest that you unplug the NUC and then disconnect the CR2032 battery from the board for 15 minutes (this battery is on the opposite side of the board and you need to remove the board from the chassis to access it (sorry)). Reconnect the battery, put everything back together and then power on and see if the BIOS will output to the monitor.
If the BIOS won't output to the monitor, then you should have the NUC unit replaced. If you can do this through your point of purchase, you should do so (it's usually faster). If you have to do it via RMA with Intel, you need to contact Intel directly, using phone, chat or email services (I recommend using phone; I *do not* recommend using their online forms service) Here are links to contact information, by geography:
Hope this helps,