Well there are a few reasons this could be happening.
1. The device is on, yet the screen isn't. In that case you would need to let the tablet run completely out of power and then plug it in to charge. Leave it charging for a few hours, and then try and turn it on.
2. The charger cord is not functioning correctly and you need to replace it.
3. The battery needs replacing.
In the case of #3, or if you can't get it to work after trying numbers 1 and 2, and if you are under warranty for the device, I would suggest contacting the manufacturer about the problem as they can then either repair or replace it. However, if it isn't under warranty, then you have the option of trying to do the work yourself (yes I know the battery isn't easy...