Even if your Quartus software was using the PMDX's port (unlikely), it would still show up in Device Manager.
I had a bunch of other questions but then I re-read your post and you say you have 3 amber LEDs that light up. Do all 3 turn on and stay on? Are these the "power", "Steps" and "enabled" LEDs? If they turn on and stay on, something is wrong.
So first thing - disconnect everything from the PMDX-424 except the power input. What do you see on the LEDs? Now plug in the USB cable. Any change?
No on to the rest of the questions:
What version of Windows are you running?
In device manager, so you see any devices anywhere with yellow question marks next to them? You may need to expand the USB section at the bottom.
The blink pattern on the green LED - is it a very short blink once every 2 seconds? Or more like same amount of time on as off, or is it on mostly and off for a short time?