I'm strongly thinking ESS to replace the C10 BOB and get rid of the parallel. stuff kind out dated. I have the Automation Technology Kl-5056D drivers and the 570 oz steppers and no it is not new.
CH
The ESS does not replace the C10. It replaces the parallel port but in the end the signals "look" like parallel port signals and plug to a BoB before they go to the motors, All you are going is adding complexity. Are you sure on the pinouts? Those look backwards.from most I have seen. Take a simple DVM and pull your DB25 cable to the C10. Write down each DIR pin that is defined in your setup. Then put your meter on DC volts and measure between pin 25 (gnd and - side of the meter) to the respective pins for each axis DIR signal. Jog that axis and change the direction. The DIR signal for that axis should go from low to high (about 3.5 volts DC on most PC's or vice versa. Bottom line you are checking for activity . Low is close to zero volts (less then 1 VDC). If you get signals than good chance the MACH is sending out signals to the parallel port.
The next thing to check is your Charge Pump. Go to Ports & Pins and Output signals and find the two charge pump ouputs. Make sure the first one is enabled and note waht port 1 pin it is on. Go back to the cable using pin 25 and the pin noted for CP. When you come out of RESET that pin should go to about 1/2 of the DC volts as the normal HIGH so something like 1.5 to 2 volts. You have to have CP on most BoB to let the signals through .

I know you are frustrated but tossing out the parallel port and setting up Ethernet and the ESS is not a 5 minute deal. If you buy your new components from the wrong vendor you will be stuck where You are now....poor instructions and asking for help on a forum.