Haha, the paper towel and Tide box computer brings back memories. My cousins and I made side-scrolling video game machines this way.

We set up the paper towel rolls in the box, with paper (half-sheets of copy paper taped together end to end) rolled around them, with a big, long scene/level drawn on it. One person would turn the crank, causing the screen to scroll while the player controlled a character which could move up and down, courtesy of being attached to a popsicle stick poking out a slot on the side of the box. The object of the game was to hit goals and jump over objects and pits.

More complex games had two popsicle-stick controlled sprites, and I seem to remember that we experimented with cannibalizing the motor out of a broken remote control car to run the screen, at one point.