The first two or three Law & Order games used QuickTime. Do you have the version of QuickTime installed that came with the game? It might not offer to install QuickTime if you have a later version, but the later version may not work with the game.
Another thing you might try is changing the screen resolution to 800x600 before starting the game. It might help to install monitor drivers for your specific monitor if you're using generic Plug 'n Play monitor drivers.