It's starting to point to the board as the problem, but wonder if it is worth checking the output from the PC parallel port.

Can anyone tell me if sfallan is OK to try the following (without damage!):
Disconnect the parallel cable from the control board, and use a multimeter to check the state of the pins on the end of the parallel cable (other end connected to the PC). Place one of the probes on an earth pin, and the other on the pin you want to check.

For the direction pins set the multimeter to DC on a range of at least 5V. I think these will change between 0 and 5V or so when you use the keyboard to move that axis. For example left might be 0V and right 5V.

This is the one I'm less sure of - for the step pins set the multimeter to AC on a range of at least 5V. I think this will change between 0V when not moving an axis and some other RMS value of the pulse train when you use the keyboard to move that axis. For example not moving that axis would be 0V and moving that axis would be say 2V RMS. I don't know what this value would be other than probably not 0V. Values will depend upon your 'steps per . . ' setting and 'velocity' setting in Mach3.

If you can show that the PC outputs are OK, and you document this, it may give you some recourse with the original supplier.

If you want to then check the board and you have access to a function generator which can create a 5V square of varying frequency you can connect this to a step pin on the board and operate the motors directly. Appreciate not everyone has one of these.