Instructions
Check the Nintendo DSi AC adapter and make sure it is properly connected to a wall outlet. Both of the metal prongs on the AC adapter need to be firmly pushed into the outlet for the AC adapter to work. Try plugging the adapter into a different outlet elsewhere in your home to make sure the problem isn't with the wall outlet.
Remove the cover to the battery compartment on the backside of your Nintendo DSi. Remove the battery and reinsert it into the console. The battery should lay flat inside the DSi, and you should be able to easily replace the compartment cover over the top of the battery pack. If the battery is inserted incorrectly, this could cause the "Power" yellow indicator light to come on.
Make sure that the opposite end of the AC adapter is properly plugged into the "Charging" slot on the top of your DSi. The small metal input on the end of the AC adapter should be plugged directly into this slot. It should not be loose, and it should not move at all when connected. A loose cable connection with the DSi could cause the yellow light to come on.