Never had to troubleshoot mine but I assume we can test as if it were a normal workstation.
open the NUC and remove all removable parts...likely just the Hdd, memory and all usb devices.
Hopefully the Nuc power light comes on and it posts. You will of course get error messages or beeps...but that would at least be a sign the the main board is working.
reattach devices one at a time and test each time.
If there is still no power at all with everything removed, you will need to get your hands on a working power supply to confirm whether yours is defective or not.
If you have a multimeter it's definitely work a shot. Not sure if the +- contacts would fit in the hole to make contact with the center of the power supply's tip.
Of course the power supplies may vary a bit depending on what generation NUC you are using but I tested the power supply on my 4th generation NUC and the contacts of my multimeter fit inside the adapter. Didnt try my 8th gen NUC because it's running critical services but I'm pretty sure the fit would be very similar.
I like to make sure it's not in a deep sleep state. Plug it in and hold down the power button for a solid 10sec (only needs 6, but time flies), let go after hitting 10 and press the power button as normal. I've had every generation from the first pre production model and this has happened more times than I can remember.
I just got my hands on this baby.