Outcome

How it works (pre-dis-assembly):

The toy is powered by a flywheel.  The flywheel is spun by a gear train connected to the wheels.  When the car is pushed along the ground, energy from the wheels is transferred through the gear train to the flywheel.  The gear train is a series of interconnected gears starting with the large gear, which spins a small gear faster, which is connected by a shaft to another large gear, which spins a smaller gear even faster.  This chain repeats several more times until the last small gear, which is connected to the flywheel.  The flywheel spins very fast because of this, and its inertia propels the racer long after somebody stops pushing the vehicle.  It also has a noise maker attached to the wheel shaft.  A toothed wheel engages a metal strip, which is bent out of the way and released by each successive tooth on the wheel, making the clicking sound.

Our assertions about the toy's structure were mostly correct.  There was a flywheel that stores up energy to make the wheels spin after the initial push.  The pieces also consists of the noise maker that made noise as the wheels spin and the separate pieces make up the car's appearance.  However, there was only one set of gears (one large and one small) that led to the fly wheel.  It is amazing that only one set of gears is enough to spin the flywheel to make the car move.  It must be because the car's structure was pretty hollow and light-weight.