http://i.imgur.com/jYv6saa.jpg?1
http://i.imgur.com/SdCGmYc.jpg?1
I know this is pretty messy and the progress is kind of scattered, but here's my full FBD of the cart. Wheels A and D are contacting the rail: 16423 N at point A and 632 N at point D.
One of the things I think Rachel missed (though her work is very impressive) is the torque arm for the tension is 1.0 meter, which is found by extending the force vector backwards until a perpendicular line crosses through point A. So the torques are as follows:
torque_gravity around A = 6396 N*m
torque_tension around A = -5448 N*m
torque_(either C or D) = -948 N*m
The final point of contact must be point D so the force on the rail is downward.
Then its just a matter of finding the force on point A by setting the "vertical" forces equal to zero.
Sorry about the messy work.