Thank you for the replies, guys!
@azrobert - Yes, can make a call with Chat; No, can not receive a call with Chat. I deleted Talkatone off of my mom's iPhone already.
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I think it's my Google Voice that is having the problem. I deleted the Obi device using ObiTalk, and then added it again using my brother's Google Voice account. With his phone number now attached to Obi, I was able to make and receive calls - it rings the phone attached to the Obi. But, once I went back to MY original Google Voice account, the one with the landline ported to it, the phone again can not receive any incoming calls, all going straight to voicemail. So, if it works with one Google Voice account, but not with the other, it's probably some kind of random error with Google Voice, right? I posted a question at the Google Voice forums, and it seems like many other people have the same problem I do. I just wish there was a more direct way to contact Google Voice help, so that they can straighten this out. If there are any other ideas, I'd appreciate it. Thanks so far, guys!
Edit: All of my incoming calls are still showing up in the Google Voice Inbox "call history". It's just not ringing the phone, and instead is going straight to voicemail.