Yes, It might be a problem of a broken
fuse, there are two on the motherboard located. Or the
chargingchip might be corupted.
On the New 3DS XL the f2 fuse located on the daughterboard is for battery power.
View attachment 339992
Solution from ifixit.com (link above) :
Check your fuses, diodes; power circuitry. The fuses (in red) should have continuity, the diode (in blue) when tested with multimeter: red lead on output and black lead on input should be OL; reversing the leads should give 0.165V (Diode test mode). Also check the resistor values, and inspect the solder joints.
The fuse for the battery power is located on the action buttons board (in red).
Replacing the fuse or daugtherboard may fixe the issue in that case.