This sounds like the battery needs to be replaced. Based on what you've said, I am going to hazard that it wasn't used for a while and then it was turned on recently? Correct me if I'm misunderstanding. But that's the perfect storm for battery failure. Even when the device is off, power is being delivered to the board, so the battery drains slowly until it is totally depleted. If left for some time in this state, the battery may not be able to charge up again.
If you disconnect the battery and try to turn it on with just the charger, does that change anything? It's worth a try to attempt to isolate a potentiality bad battery from the equation. It may not be able to power on at all without the battery, but it won't do any harm to check.