It looks like the FL inverter (backlight) is failing.
An LCD screen is made of several components, the important parts are the actual LCD, which makes the image, and the backlight, which shines through the image making it bright enough to see.
The LCD part of the screen is usually very hardy and will normally last a very long time. The backlight bulb: not so much.
Normally, power management can turn the backlight off to save power. When the backlight goes off even when the computer is being used, that usually means it is failing or broken.
Update your drivers, the system BIOS and all such stuff like that, but if the issue continues, you'll need to get an external monitor or replace the computer.
It's an old computer and repairing a backlight usually costs several hundred dollars.
Another possible fix is to find another laptop of the same type that is used and say had a power problem or the CPU is dead, buy it cheap and swap the screen onto yours.