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Yes that's totally normal, the screen will end up completely dead at one point. All LCDs, to this date, will do that. The cold cathode will not last for ever. But if your of the DIY type it is fixable (see LCD Backlight Quick Fix as featured on hackaday.com). Although this is a large LCD, dunno if part would be available for the much thinner laptop screens, but I wouldn't be surprised if they are.