You probably have a couple of things going on. First the paint has filled the recess of the screw head making it hard for the screwdriver to get a good "bite". Then the paint is sticking the screw to the hinge.

Start by cleaning out the screw head really well. Use a utility knife or other small, sharp tool to remove the paint being careful not to damage the screw head. If you don't care about the hinges, a small wire brush in a Dremel may be useful too. Then take the knife and cut through the paint where the screw head meets the hinge.

If the screw are hard to budge, avoid using any kind of power tool. Instead use a regular screwdriver to get them started. If you're having a hard time, add some leverage. If you have a square shank screwdriver, use an adjustable wrench. For a round shaft, a pair of Vise-Grips. Push very firmly with one hand while turning the wrench with the other. Sometimes working with another person helps. One to push, one to turn. Once you've broken the screw loose, use the drill.

Good luck!

Mike

Thanks Mike! I will try your suggestions today, first I'll have to buy a regular screwdriver. I will put away my trusty electric drill for now.

My DH taught me a great trick. Take a regular screw driver and a hammer. Put the screwdriver in the painted slots and hammer away until the screw driver breaks through the paint. That way you will get a good bite. When you try to turn it to losen the screw press IN _really_ hard. It seems counter intuitive to press in when you are trying to get the screw out, but it really works.

...and use a boxcutter or razor to cut through the paint all around the hinge where it meets the wood. That way the hinge will come away without taking surrounding paint layers and, possibly, wood away from the cabinets.

the screw head of my cupboards where completely filled up with paint to a point that some screws were hidden. So I chipped out the paint with a finishing nail and a hammer until I could fit the screwdriver in the hole.