My 3ds lights for a time but never charge

On the bottom of the 3DS console, there are 2 small screws. Under them, you can find the battery compartment. Try removing the battery and holding in the power button. If this does nothing try replacing the battery as they are relatively cheap. Opening this cover will not void your warranty but if the system is relatively new if that doesn't work send it in for repair as it will be under warranty.

I cant really think of anything other than a connection error that would cause this so if your system is not under warranty you can open the screws below the cover previously described. Inspect the board for any broken solder joints or loose wires and connections. You can simpily fix the loose connection by resoldering this stuff but be careful as it is small and delicate.