You will need to have some fairly serious DIY skills or someone with such skill because this remedy requires a bit of accurate drill work. I recommend that novices practice this technique on some scrap timber first.
First, mark the original position of the hinge so it's in the right place for marking the new screw holes. Find or buy a 6mm dowel for each srew hole needing repair (such as those used to join cabinet pieces).
Put a 6mm drill bit in the drill chuck and drill through the length of a piece of timber approximately 25mm square and as long as the bit. remove the timber and cut off 12mm, replace the timber on the bit, this will act as a depth gauge allowing only 12mm of drill bit to penetrate the door.
Holding the timber with your spare hand position the drill over the damaged screw hole, (resting your knuckles on the door will give more stability) and switch on the drill, the timber gauge and bit may squeal a little but don't let it worry you, it's natural.
With a firm grip on timber and drill, lower the rotating drill bit into the damaged hole and firmly drill it out. put a little PVA wood glue in the new hole smearing a little around the dowel and, with the door on a flat surface, gently tap the dowel into place, wipe off excess glue and allow to set for ten or twenty minutes.
When dry the protruding dowel can be carefully sawn off. You then need to refit the hinge and mark up for the new screw holes. I suggest a 2mm drill bit for this, drilling to a depth of approximately 4 or 5mm and fit the new screws. Repeat as required and good luck.
Ken the cabinet maker
August 2011