laptop batteries have a number of cells usually 4.
once they are dead they are useless, this can happen suddenly.
try a different battery. does it work on the power supply with the battery removed.

if the battery cant quite supply enough the display might not work this might be because the laptop knows the battery is very low.

or

the LCD screen brightness has been set too low, there are some laptops that have reported problems with setting the screen brightness when the laptop starts, back to almost zero, so the screen is on but you cant see it. Try adjusting up the brightness.
also try adjusting it up in a very dark room and see if you can see the screen then.

this affects certain makes and models and may need a bios update to fix it

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