How long does the screen take to become normal operable backlighting? You're sure it's not your eyes adjusting to the screens lower brightness? Have you tried upping the brightness of your laptop screen when powered by the battery? There are shortcut keys located anywhere on the arrow keys or the function keys which are accessible after depressing the Fn key and the key to adjust your brightness.
e.g:
To add more to advice, you might also want to open Power options(from Control Pane) and adjust the minimum brightness settings when running on battery as opposed to a charger/plugged in.
It'd be a good idea if you could pass on the SKU for your laptop.