Well first I would suggest holding down the power button for a bout 20 seconds and then try plugging it in to charge. Sometimes, if the battery gets down to 0% they just don't like to start again. At least not without a little push. Hence what I stated here.
If that doesn't work, I would then test your charger cord to see if it is actually working correctly. The smartest way is to use the cord on a different device. If it doesn't charge that one (and it is a cord it can use) then the cord probably needs replacing.
Your battery may also be going. They do after a while. So if that is the case, it would also need replacing.
Another thing to check is to make sure there is nothing in the port on the device. As in dirt, dust, food, lint...