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Try to drill at the top of the screw (if it's the bottom screw; or drill at the bottom if it's the top screw) so that whatever hole you make can be obscured by the hinge flange when you put the hinge back on.
As far as the larger hole thats left after you get the screw out, use a little bit of wood filler to fill it up. Drill a small pilot hole once it's set up and hardened and drive your new screw in gently. It's worked for me before in a pinch.
[This message has been edited by JayF (edited February 27, 2003).]