The tablet is not meant to charge without battery.

Regardless of charging, does it boot wit the charger plugged in?

Is the sw original?

If it is some 2nd hand tablet, try flashing the original image.
Even if it shouldn't boot, it doesn't automatically imply that it will not be possible to flash it.

If you are sure you are running the official sw and cannot charge, one of the parts is probably faulty (the tablet, the battery or the charger).

Being able to boot with both the battery and the charger plugged in means that you have a problem either with the battery or with the tablet, but not with the charger.