Probably just something wrong with power to the backlight. I don't think the videocard has anything to do with the backlight...if it did, I'd think you'd loose power to the whole monitor, not just the backlight.Usually laptop monitor cases are easy to get into. Screws are usually hidden behind the rubber stoppers and other obvious covers. Pop the cover open and have a look at the ribbon connectors and make sure everything's snug.
It could even be the backlight itself, which is kind of a worse-case scenario. To my knowledge, you can't replace it without replacing the entire LCD unit. Might be able to find one cheap used, though...check with local used laptop dealers in that case. I got a replacement keyboard and good battery for $40 because the shop just happened to have a burnt-out laptop of the same model in the back one day.
You can always try and figure out which wire is power for the backlight and see if it's getting power. If it is, and the backlight's out, you know it's the light itself. If it's NOT, you need to figure out why not.
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