The Ion battery could have died completely meaning that it can no longer charge. Much like a rechargable battery; you can keep recharging it, b ut it will eventually use up all of it's energy. If y You may have charged it enough to kill the battery. Like any rechargable battery, it will eventually not be able to recharge anymore after a certain number of uses. If this is the case, the DS won't turn on because there is no power to supply it. You can find another ion battery the same size the DS uses and try to replace it yourself, but opening the DS WILL void any and all warranty.
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On the right side of the nintendo, there is a switch and you have to push up to turn it on. Make sure you charge it so it can turn on.
You pull the battery out and put all the parts in a bowl of rice which dries it out.
turn off the ds before it runs out of battery and it charges extremly slow but it charges
Try using different outlets or a different charger. If this doesn't work, you may need to have your DS repaired of replaced.
Check to see if the battery is securely placed. If it is, then plug the DS into the charger and connect to an outlet. Then it should charge up and work.