Could be a dead battery, meaning it's completely fried and needs to be replaced.
Lithium-ion batteries are only good for so long, and eventually they lose the ability to hold a proper charge. It may say the battery is charged, but it's only showing a full capacity because the cells are so worn out they can only hold a very small fraction of what they used to be able to.
Test the phone with a friends battery, if it turns on then you know for sure.