This will work, trust me. If you have access to a mig welder...
Clean the paint off the heads of the stuck hinge screws. Find a shallow
nut, the I.D. of which is judt a tad smaller than the head of the screw.
Center it over the head of a stuck screw, and mig weld it securely to
the screw head. Let it cool and use the hex to back the screw out. If
the nut breaks loose try and try again. Sooner or later, you WILL get
it, and the threads in the body should be OK.

It works because the heating-cooling cycle breaks down the rust bond
between the screw and the captive nut. Same procedure works to remove
broken studs from engine blocks. I hardly ever drill a broken screw
anymore, because the mig welder method is easier, faster, and less
likely to leave you with damaged threads in the other part.

It takes less time to do one than it takes me to type this.

BTW, if the hinges screws are in just normally tight, and not corroded
in place, it really helps to use a quality screwdriver bit that fits a
3/8" drive socket set, and then dip the end of the bit in coarse valve
grinding compund. The grit really improves the grip between the
screwdriver bit and a tight screw.

Good luck,

Gordon Richmond (mercyless screw destroyer)
----------------
AND WELD THE INSIDE OF THE NUT (THREADED AREA) TO THE HEAD OF THE SCREW !!!!!!!
 it works great and comes off with a socket, I have seen it welded on the
outside and now all is one piece (screw, nut and hindge) .