Hi:
Getting your wife an OBi for Christmas sounds like getting her an ironing board or vacuum cleaner. And, when it seems to have stopped some existing good thing from working (ringing Hangouts), I can just imagine the spousal discord.
So, let's try to figure this out. Hangouts works independently from the legacy Google Chat protocol that OBis use. As long as you (or your wife) are logged into Hangouts on any Hangouts client (laptop/desktop via Gmail, via the new Hangouts Chrome browser web app or extension, or via Google+), or via an Android or iOS device, any/all logged-in and enabled Hangouts clients will ring. Using an OBi should have no effect on that.
You can unplug the OBi to confirm this.
Using a computer, with the current stable or beta version of Google Chrome Browser, go to Gmail (not Google Voice). Look for your chat avatar along the middle left side of the web page. It's either a generic head and shoulders icon or a photo you uploaded. Look at my attached screenshot. If it looks like that, then you are using Hangouts. If not, then you're using old Chat. In that case, click the icon, then click the "Try the new Hangouts" link. Once you are using Hangouts, then click the small down-arrow next to your avatar to open Hangout settings. Make sure that receiving inbound calls is enabled, per my second screenshot.
Optionally, you can install the Hangouts web app from the Google Chrome web store here:
https://chrome.google.com/webstore/detail/hangouts/knipolnnllmklapflnccelgolnpehhpl?hl=en