[lawgolfer]

You will never get an "E-Z Out" into a little cabinet screw. Your best hope is to remove the other screws and hope that enough of the broken screw remains above the surface that it can be caught by a vice grips pliers. If you can't get the screw out, you'll have to move the hinge just enough to cover the broken screw.

It will be much easier to remove the remaining screws if you can apply some heat to them first . I would use a "mini-butane torch" which puts out a pinpoint flame. Put duct tape around the edge of the hinge to protect the finish of the cabinet and focus the flame on one screw at a time, first touching the screw head then removing the flame to let the heat "sink"into the shaft of the screw, and repeat.

With the door being fiberglass, this is going to be tricky.

The final thing is to use the largest screwdriver which will fit the screw.