How to remove a broken computer screw?

Drill the head off the screw or Something from here

If it is a screw with a cross-head, that is worn down, you could try it with a tiny hex-key link .

Here is what I would do..

I would use the epoxy in two tubes that you mix. Then I would use a toothpick to put a tiny amount on the tip of the screwdriver. Find a way to hold the screwdriver on the screw while it cures. Remove the the screw. That shit is crazy strong.

I used the epoxy stuff to mend a fan clutch. It lasted for about an hour before breaking and destroying the radiator.

The head is still intact, right? You can try cutting or fixing the slot by using a good, hard screwdriver and tapping it with a hammer gently sideways though the slot. Often that will reshape it enough so you can get a properly sized screwdriver in place. After you’ve “fixed” the slot, put the correct screwdriver in place and tap the handle straight down. That will seat it better and loosen any locktite that might be holding the screw.
Drilling it out is the last resort.
(Cutting torch is really really the last resort.)

This sometime works for me when I have a stripped screw head. Try placing a flat rubber band between the screw and the screwdriver. This should help with the resistance problem. Use firm pressure and slowly try to rotate. The rubber band acts to fill in the space that the screwdriver can’t grip.