Control hacked servo motor speed using L293D and PWM
Based on your (further) info, if there is no control wire, I think the reason it is not moving properly is that what you have now is basically a DC motor. 
To control a standard DC motor with PWM, you simply use a duty cycle between 0% (off) and 100% (full speed) 

The current needed will be a lot higher than a servo control wire, as rather than controlling the feedback, you are controlling the actual power to the motor. This is okay as you have the L293D though, which will supply more current than a uC pin can, and exactly what they were designed for.

I suspect that the 2ms is too low to provide enough power to start the motor turning - if you have a 20ms period, 2/20 = 10% of full "power" (roughly - note actual power is I squared R, so at 10% will actually be 1/100th of power at 100% - RMS voltage would perhaps be a better term here) Try a higher value and see where the motor starts reliably. Let us know the results.

Here is a page that explains the differences quite well:

Dc vs Servo