It is possible to connect a PS2 to a laptop, as long as the computer has a compatible port built in. Ports that allow AV input include VGA, DVI or HDMI. A switch box is also required for the signal from the PS2 to show up on the laptop monitor.
To complete the connection, plug the switch box into the computer. Connect the red, white and yellow AV cables from the PS2 to the matching color-coded ports on the other side of the box. Press the option button on the laptop monitor and choose the port the switch box is plugged into to play the PS2 on a laptop.