That does not sound good.
You can try the FLIR One G2 trick of plugging the unit into the charger and holding the power button down for a few minutes. This used to work on some units.
It almost sounds like the battery protection circuit is being activated and isolating the battery. If you can get some charge into the battery either via the power button hold down trick or by removing the battery and charging it externally you may recover the cameras normal operation.
If you can send the camera back for a refund or exchange, I would do so, it sounds like a charge controller and battery protection issue. Such was common on the F1G2
Fraser