It would be unlikely for the other axis to induce movement in your x-axis.
When you are running the tests, is the X-axis 'locked' (you can't move it by hand)? It should be locked.
The inputs are pulled-up with 10k resistors, so it might be possible for some input noise to move the axis (but also unlikely).
I assume no change to your 40V power supply, but you didn't mention the current capability - how is this voltage holding during your test?
Tell me about the parallel cable - same, changed?
What about how your setup is grounded - potential induced noise or ground loop causing noise to the x-axis input?
Is the parallel cable physically close to any of the stepper motor wires?
Are all your power supply connections firm/solid?
BrianV