Are you allowed to dissasemble toys ?
How about using one of those "zip tops" type of things where a long plastic thing (zip strip) with teeth on one side slide through a small whole and travels against a gear providing rotation. Or an actual SSP car if you can find one.
Or put rubber (rubber paint or a tight elastic band) around the top itself, and use it as the tire.
The top might be usefull as the flywheel.
Like these old cars (SSP mentioned earlier)
http://www.bigredtoybox.com/cgi-bin/toynfo.pl?sspindex
Just a thought.