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, etc., and that nothing is bent in it. Any of this can interfere with charging.
If, the port is loose on the device, then that is a whole other issue. In that case the entire motherboard may need replacing, as the port is attached to it.
If your device is still under warranty, I would not suggest trying to do that last one by yourself, as you would void the warranty. If it is under warranty, then check with your service provider or the manufacturer.
Another 'possible' issue could be an app. Some apps can wreak havoc on battery use and charging. If you want to test if it is an app you would need to try an load the phone in "Safe Mode" to do so. (of course it would have to be charged first.)