Getting the small hinges screws (broken) out of the timber

I made the mistake of using the screws that came with the small hinges for a box that I am making. The hinge itself is only 1" (25mm) in width so you can imagine how small the screws are. Anyway the slots went and when I tried to get the screws out, the shafts broke. Any of you experienced chaps know the best way to get the screws out without messing up the box. The timber width is 3/8" (9mm approx)?
Many thanks
Paul