If you're using L293's then you're wiring your motor in bipolar mode. If you want to use discrete transistors then you're either trying to wire it in unipolar mode or you're trying to build two H bridges to keep it in bipolar mode. You'll need to explain.
With the L293 wiring it should move even if you're not able to supply it with the 2A it needs -- it just won't have its full torque. More than likely you just have the wiring wrong, but if you did have it correct then you probably burnt the L293 when the stepper tried to draw its full 2A of current.
...and so that refers to your questions, but here's your advice:
Using transistors (or an L293, which is transistor based) is using 1990's technology; there are much more modern solutions available. For example, a module based on the DRV8825 is cheap and capable of 2.2A when using a heatsink, but those modules allow you to ramp down the current to keep the heat in check. It really comes down to how much power you need from your stepper motor as to what you should be using but you'd need to give a full description of your project for that type of advice.