Okay I do not quite get what you mean here, but I have tried the method you recommended: to disable the DHCP Server on my ASUS router. The result is that now the NAS cannot be detected at all, by both the D-Link storage Utility and Net Scan.
Some additional information, I did have a modem in use, which is provided by my internet service provider, Pace 2Wire 5012NV-002.
My router was reset recently, and in its latest firmware. The only configurations were setting password for WIFI and turning on some basic security features.
As for the NAS, nothing was changed ever since it has been out of power and back in use.