Did you connect the Antenna while the NUC was ON? This could have caused a short and damaged something on the hardware.
My best recommendation is to clear the CMOS on the NUC. Here you have the instructions:
Besides this, try connecting just one memory stick on the system for testing purposes.
Thank you kevin_intel for your answer.
I have tried removing each memory memory stick one by one, with no success.
I also tried clearing the CMOS, but I failed at step 6 (Power the computer ON) here : http://www.intel.com/support/motherboards/desktop/sb/CS-034524.html. At that point, nothing happened. No light was turned on and the fan was not active. There was no sign of activity.
I might have caused a short and damaged a hardware component, as you suggested. If it is a fuse or a simple component, I am more than willing to change it myself (the warranty on my NUC has ended long ago).
Any other suggestions?
Thanks for the help,