Thank you for all the suggestions, everyone.

 

The two processors and touchpanel are all on DHCP, plugged into the same switch. Their gateway/subnet mask information are all received from the DHCP server and therefore are the same. I can reach the touchpanel with no issue. 

 

dblpnt - This looks like the right answer. I'll have to wait until I'm onsite to check, but this makes perfect sense!