broken screw

i am installing new under stairs storage and have installed the doors.One of the screw heads broke off and I am left with a partial screw in the wood and no head to remove it. what is the best solution to remove the broken screw and remove it to replace it with a new screw that hopefully will not break !!!!
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In an earlier contribution to this discussion,

Can you get at enough of the shank of the screw to grip it with Mole grips? If so, that's the best way to get it out.
If not, can you get at it enough to cut a slot across the top of the shank with a hacksaw (or maybe a Dremel) and then use a screwdriver on it?
If all else fails, you may have to drill a small hole (1 or 2 mm dia) down the middle (easier said than done!) and then use a screw extractor on it.
Or - if it's one of many hinge screws - just ignore it. The remaining screws will probably support the door adequately.
--
Cheers,
Roger
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Without seeing the job it is difficult to advise, but how about digging the broken screw out, then drill a hole the diameter of a dowel, apply glue to dowel and insert in hole, level off if necessary, drill pilot hole in dowel for new screw, insert new screw?
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