There is a long discussion about that board (or a similar one) at http://www.cnczone.com/forums/genera...y_chinese.html
Some people with that board have suggested various circuit modifications or improvements, while others report that their boards work fine as is.
Do you have at least some background in basic electronics and do you have access to an oscilloscope (or, at minimum, to a multimeter)? If not, do you have a friend who does?
The discussion linked above includes some schematics showing the unmodified (as well as the modified) circuit for the board. I would start out by checking the voltage output from your parallel port to see whether it puts out 3.3 volts or close to 5 volts (some people have reported problems when the parallel port only puts out 3.3 volts).
Then I would attempt to verify that Mach3 is configured to put out (and is putting out) the step and direction signals on the same pins of the DB-25 that the TB6560 board is expecting. Then I would try to verify that the step and direction signals are present at both the inputs and outputs of the optoisolators on the board (many people have reported problems with the optoisolators being "slow" or otherwise not passing the signals through properly).
What is the Mach3 kernal frequency setting? Start with 25,000 and see it if works there.
What are your dip switch settings? What are the current and inductance ratings of your stepper motors? How did you choose which stepper wires to connect, and how to connect them? Did you rely on a datasheet or a color code or did you probe the motor windings with a multimeter to verify them?