you say your screen is burned out, but you don't say if your computer boots, either from the internal HD or from an internal or external DVD unit, using a Linux live-CD/DVD for instance
This would allow, connected to an external screen, rather than taking your hard drive out of the case, to copy the contents of your drive to an external USB hard disk ?
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== Update ==
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If you see leds blinking and hear some clicks when you turn your computer on, it means it probably boots.
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Try to find and connect an external screen. There should be an external screen connector on one of the edges of your laptop (probably the rear one). Every laptop has such connector, and a control key to switch from internal screen to external, and to both of them, that's very useful for people performing Powerpoint (or equivalent) slide shows. I am not a Mac user, but the user manual probably says how to switch screens.
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When you have your external screen, computer powered off, connect the screen, turn it on, and then turn/push on your MBA. If you get at last a display, you are more than half-way to your data :-)
hello
you say your screen is burned out, but you don't say if your computer boots, either from the internal HD or from an internal or external DVD unit, using a Linux live-CD/DVD for instance
This would allow, connected to an external screen, rather than taking your hard drive out of the case, to copy the contents of your drive to an external USB hard disk ?