I'm sure the Fred Flintstone method is a hoot to watch, but believe me, it gets old the first time you forget the brakes don't work right.
As to how it is moving, I really don't know - I suggest looking at the wiring diagram and making sure everything is wired like it shows. That's the first place to start, then troubleshooting by conventional methods can start.
Here's the diagram for your cart:
http://www.buggiesgonewild.com/attac...e528185if2.jpg
as well as the solenoid wiring:
http://www.buggiesgonewild.com/attac...6solenofh6.jpg
Hope this helps!