Has anything happened recently, such as a drop, contact with water or a repair attempt?
If nothing out of the ordinary happened recently, then you could have a defective/dead battery or perhaps the charging circuit on the logic board was damaged by a cheap, dollar store charger.
You could try to replace the battery yourself by following this [guide|45222|guide] up to step 24. Note, this requires some soldering. If it is a logic board problem, then you may need to have this looked at by a micro-solderer.