What's "hinky" is exactly what DrGeoff described: a problem with your house wiring. If the phone (via its base station) rings when plugged directly into the OBi, then the phone and the OBi are both working properly and don't have any role in this failure.
Either your house wiring is still connected to the telephone company's outside wiring, or there is a poor connection or wiring error somewhere in the wiring in the walls. If you have the electrical troubleshooting skills to trace the connections throughout the house, you should be able to find it.
In the USA, depending on when the house was built, there is typically a multi-conductor cable running through the walls, and then each phone jack is tapped into those wires in a "daisy chain" or parallel fashion. Two conductors are used per line, known as "tip" and "ring" (these terms refer to an old telephone switchboard phone jack, with a metal tip, and then an insulator, and then a "ring" of metal). I attached a diagram below.
There are three states that can exist on each two-wire pair: on-hook, off-hook, and ringing. On hook is roughly 48VDC, and off-hook drops to roughly 12VDC. Ringing, as Geoff pointed out, superimposes a ~70-80VAC signal over those same two wires. In the olden days, that AC voltage caused the electromechanical bell coil in the telephone to move the little metal striker against the bell. Nowadays, it just tells the integrated circuit in the phone to generate the ring.
Bottom line, the two-wire pair needs to be solidly connected, with no corrosion or breaks, and no mistakes in wiring, such that it is crossed with one of the other wire pairs.
If this is too hard to troubleshoot, just abandon the house wiring and use one DECT 6.0 cordless base station with as many handsets as you need around the house.