Just bought a new laptop Dies whenever it's unplugged

Shutdown the laptop. Remove the power supply. Remove the battery. Open the lid and press the power button 10 times and on the last time, hold the button down for at least 30 seconds.

Close lid, re-install battery, re-attach AC supply. Power up laptop. Observer the battery charge status indicator - is it amber (most will be amber/orange when the battery is being charged).

When the laptop powers up, check on the tool bar and see if there's any indicators on the system tray indicating the battery is charging?

The unplug/remove battery / 10 power button press trick has worked on IBM/Lenovo Think Pads and at least one Toshiba laptop.

If the above doesn't work, I'd return the laptop as defective.

Exchange for another one since you just bought it.

Bring it back for replacement. Defective product…

Battery is dead or hasn't been charged for 8 hours BEFORE use

Battery is probably messed up.