Called D-Link Tech Support. They blamed the printer for my problem.
Here is the problem:
CAN print to the printer when connected via ethernet to the D-Link router.
CANNOT print to the printer when connected via WIFI to the D-Link router.
If I substitute a different WIFI router for the D-Link Router, everything works.
When attempting to print from a Mac connected vie WIFI to the network, I can ping the Brother printer, but the Mac cannot connect or print. If I plug in an ethernet cable while it is "searching" for the printer, printing commences.
Sounds like a router issue to me, not a printer issue.
Solution: Buy a different brand of router. I simply don't know what else to do.