Check and see if someone else has a better/safer solution first, but this is what I did when I had a screw break on an old computer back in the mid 90s:
Get a push pin (one with a colored plastic push part and a metal pin). Take a pair of snips and cut the point of the pin off. You may need to get a small metal file and file down where you cut the pin so you have a flat surface.
Next, take some super glue and put a VERY small dot of glue on the tip of the pin where you cut it. Now, VERY CAREFULLY, match the head of the pin up to the broken metal screw. BE VERY CAREFUL not to get glue on the threads or you will just glue the broken screw in place!!! After a few minutes of holding it still, slowly twist the screw out. (This is why I suggest one of the push pins with the plastic end rather than the ones with the flat metal "disk" at the end of the pin ... you need something to grip.)
If you did it correctly/carefully, you'll remove the screw.
Again, this is very dangerous and you run the risk of gluing the screw in place. So, check and see if someone smarter than me knows a safer way.