The electric drill will only seed up the stripping process.
Get up close to the screw. See if there are metal bits clogging what's left of the screw head. If so clean them out with a small pointy tool like an icepick. Then make sure the screwdriver is well seated in what remains of the screw head. A light tap or three can help here. Keep the screwdriver well aligned and pressed in tight while carefully turning .
If it is well and truly stripped you may have to cut the broken plastic part away from it and grab the screw with locking pliers