Wawa:
The burned part is a 4.7uF/16volt tantalum capacitor.
A bypass capacitor on the 5volt rail.The Nano should work without it (remove it), unless you have connected a power supply with reverse polarity to the 5volt pin. Or maybe inserted the Nano the wrong way in that shield. In that case everything will be toast.
Leo..
Thank you WAWA. I placed the NANO with the USB connector jack facing the same side as the power Jack of the shield and before connecting it I compared the markings of the shield and the NANO.
Thanks