Transmission does not shift to 2nd grear, moves forward on R position

I think you have an internal problem, but better get your meter and check the 'Inhibitor Switch" (Mazda doesn't call it a "Range Switch," FYI). You could get a wiring diagram and check the inputs and outputs (carefully) from the controller to the transmission. I'd suspect the trans internal parts, like a failed solenoid. There would be no signs of this kind of failure except on internal inspection. I think it's unlikely that the controller failed in this manner. Is your check transmission light on? There would be a clue there. Go to a transmission shop or a Mazda specialist for more information. Here's a directlry link for you: http://repairpal.com/mazda-repair-in-columbia-missouri