PSP fat and PSP slim both can play PSX games that is no problem.

PSP fat does not support AV out so no ways you can play it on an external display.

PSP slim you can attach the AV cable (purchased separately) and play it on an external display. BUT LAPTOP wise, it depends on whether your laptop accepts an input to display, most laptops only does OUTPUT, either VGA, DVI, or s-video.