Like Bill said, if the account is properly configured, then it will work. Since you are the domain administrator, you're the only person that would know how your Apps control panel is set. See the linked help article for more details. Essentially, you must have the old Google Talk/Chat system enabled for all users, not just Hangouts.
Why not do a quick test with the failing account, just to remove any doubt from your mind on this point...configure that account on your OBi phone, and see if it works properly.
I do think you've got some sort of network issue at that location, but I don't have any advice as to how you will be able to diagnose it, beyond my original suggestion to temporarily remove the WiFi dongle, power-cycle everything to clear out the ARP cache, etc, and try it on Ethernet. If it's consistently failing, you may have a firewall rule blocking the ports to GV, or perhaps that ISP is blocking it (which I believe is now illegal under FCC net neutrality rules).