Frankly, this post confused me even more, rather than clarified. If somebody jumps in and answers - don't bother explaining to me. Until then, let me try to guide you.
The problem you are describing happens without WiFi, correct? I realize that there is also a problem with WiFi; but that problem is not in scope of your question? If correct, then any sentences describing WiFi are irrelevant, even though you are getting IP address through WiFi. If incorrect - then my next questions are irrelevant.
You plug WAN port of OBi into Router LAN port, and OBi doesn't get IP address, while other devices get IP address from the same router (I have no idea what you mean by "When I wire to LAN"; so I rephrased it in the words that I understand). Correct? And you are sure that it is WAN port of OBi, LAN port of the router, and OBi is set to DHCP. Please convince me why you are confident in all three.
Once you confirm all three (and only after that), find out through IVR what is IP address of the device and what is OperationMode. We'll go from there