With a screw that small a technique which often works is firstly to find the right screwdriver - note that there are at least two cross head types and Posidrive don't reliably fit Phillips and vice versa. Laptop is likely to be Phillips.
Clean both the screw head and screwdriver end thoroughly with Isopropanol (this wont hurt any components). Let them dry. Put a tiny drop of Superglue on the screw head (you do not want any spilling over the side of the screw head) and insert the screwdriver. Press down firmly and maintain very firm pressure without moving the screwdriver for at least a minute. Without letting up on the very firm pressure turn the screw to undo.