Should be pretty easy to switch over. Your existing board is just a simply isolated parallel port breakout board - 1 screw terminal for each signal on the PC parallel port.
For your stepper motor drivers, see:
https://faq.pmdx.com/index.php?solution_id=1010and follow the suggested connection scheme for the SmartBOBs "Ground Common". Also see the linked article about connecting the ENA signals.
For each motor, take the wires from the existing breakout board and connect them to the PMDX-424:
P2/P3 to Motor0 Step and Dir respectively
P4/P5 to Motor1 Step and Dir
P6/P7 to Motor2 Step and Dir
(if you have a 4th motor) P8/P9 to Motor3 Step and Dir
If you have any of the P1, P14, P16 or P17 terminals with wires connected, figure out where the wires go and I can give you an idea of where to connect them. The PMDX-424 has only 3 general purpose outputs, with a 4th output controlling the on-board relay.
If you have an EStop signal, connect the EStop switch between the "EStop" and "Gnd' terminals on J14 (if the EStop switch is normally closed). If the EStop switch is normally open (not usually the case) then connect it between the "Fault" and "Gnd" terminals.
For the other input signals on P10, P11, 12, 13 and 15, move them to the PMDX-424's isolated inputs 1 to 4 on J16 (and/or 5-8 on J17), with the GND leads all tied to the GND terminals on J16 and/or J17 - NOT the "gnd" pin on any other connector.
In Mach4 - I suggest making a copy of the PMDX-supplied sample PMDX-424 profile. Start the Mach4 loader, click once on the "PMDX-424-Sample" profile to select it then click the "Copy Profile" button. Name it whatever you like, and leave the "screen set" line blank. Now open up the profile that you just created. It should already have the X/Y/Z axis mapped to Motor0/1/2 respectively and the EStop configured. You will have to play with the motor tuning to set the actual steps/inch or steps/mm, plus max speed and acceleration.
You will also need to figure out what limit and/or home switches are connected to which inputs, and configure them in Mach4. Go to the Mach4 "configure" menu then select "Control". Click on the "Input Signals" tab and scroll until you see things like "Motor0 Home", "Motor0 ++" (positive limit switch), "Motor0 --" (negative limit switch), etc. If you have both a positive and negative limit switch for an axis wired to a single input, set both of those entries in Mach4 to the same PMX-424 input. Or you might have the positive limit switches for all axis to a single input pin, and all negative limit switches to another input pin. If so, map Motor0++, Motor1++ and Motor2++ to the same input pin, and Motor0--, Motor1-- and Motor2-- to the other input.
If this general advice gets too confusing, post a list of all the connections to your current breakout board and tell us a bit more about your machine. For example, 3 axis? 4 axis? Is there an axis with 2 motors driving it? Is there a spindle motor under PC control? If so, it is simply on/off? Or is there a speed control of some kind. How are your limit and home switches configured? Any other inputs or outputs (coolant pump signals, etc.)?