Difficult to say. First of all I would recommend checking the BIOS version.
Be sure that your BIOS is up to date.

But did you notice this issue from first day of usage?
Theoretically the battery should be detected even if the battery is discharged…so I’m wondering why the battery indicator is not ON. If the battery would be charged, the indicator should lit orange. If the battery is fully charged, the indicator should switch to blue….

Anyway, I think you cannot run some test because you don’t have important and necessary tools… I think new battery should be tested with the notebook and if this would not solve the problem, the motherboard should be tested too.