Difficulty unscrewing laptop case

I am currently attempting to open the laptop case because a metal hinge piece has broken off and the piece sawed the display cable open, so I would like to remove the display and use the VGA port instead. However, I need to open the case in order to remove the cables connecting the display. There are three screws on the bottom half of the laptop that I am having difficulty with. One of the screws wiggles but will not come out, no matter if I try unscrewing it further, try removing it with tweezers, or try turning the laptop around and shaking it to make the screw fall out. The other two screws will not turn when I try unscrewing them, and sometimes I can see metal shavings on the end of the screwdriver. I am using the size 0 Philips screwdriver bit. Any suggestions for removing the last three screws?