Is my computer the problem, or my graphics card?

It is your Video card that is weak for this game. You obviously have a laptop. Laptops are not the best platforms for modern games really. Laptop video cards are integrated to either the processor or the motherboard and therefore not being dedicated are no where near as powerful as desktop dedicated video cards. If you really want to play MW2 properly, use a desktop PC with a good video card and you won't have any graphics problems on highest settings.