Ok, what appears to have been the final resolution on both the Windows 7 and Windows 10 builds:
1. Create a new profile on each OS and migrate all data to that profile.
2. Making a new profile alone turned out to be only a temporary fix and problem returned.
3. Find updated NIC driver online from Realtek site, not from ASUS site for this z-87a motherboard. The driver on the ASUS site for the motherboard is old and has the problem.
After moving to a new profile *and* updating the NIC driver, the problem is resolved and DeskScapes 10 will go online on both Windows 10 and Windows 7.
Although this seems to be closely tied to this model motherboard and integrated NIC, hopefully this information may prove helpful.
Thank you for all of your help in figuring this out!