Many good suggestions. If the screw is broken flush with the eye, I would first centre punch it and try drilling it through with a 9/64 or 5/32 drill. The drill will quite possibly catch and drive the remainder of the screw right through. If you haven't removed broken screws before, it's probably better to get someone experienced to do it.
John Betmanis <johnb@oxford.net>
Woodstock, ON Canada