VOIP phone with Motorola gateway?

No

Thank you. So I have no option other than to use a POTS telephone on my Internet account? Do I have to endure being treated like garbage by AT&T's atrociously bad "customer service" and pay a exorbitant amount of money to be able to use a VOIP phone?

You can get a service like Ooma, Vonage or Magic Jack where you plug your phone into their ATA. Which amounts to digital service from another provider. Or you can opt for one of the wireless home phone services, All are less than what you're paying for the phone service out of your modem, which is not POTS. You said VoIP phone, which is a 4 wire phone that plugs into an Ethernet port and communicates with a VoIP server or hosted service.

Hmmmm ... does AT&T sell just Internet service? Without phone or TV? Some years ago, I checked into that and I don't remember just plain Internet service being offered. I'm not sure what kind of signal is coming out of the modem, but it is only on two wires. White-blue, white-orange and white-brown go into the "Broadband" port and white-green comes out of the "Tel lines" port, which is spliced to the red-green which goes to the RJ11 jack. White-brown is not connected in the ONI. The cable from the ONI to the gateway is split - three pairs to the "Broadband" port and one pair connected to the "Tel lines" port via an RJ11 plug. Maybe I should call Vonage to see what my options are. I'm positive I'm not the only unhappy AT&T customer!

The best answer to that would be call as we don't know what Internet service you have. In general, yes you can get Internet only. Sounds like you have some type of bonded pair DSL service from your description of the pairs used and what they're terminate to.

If your phone service comes directly out of the modem than you have a modem with an ATA (analog telephone adaptor) which is what the other digital service mentioned are. 

I have AT&T Uverse service which uses two bonded pairs due to the distance from the VRAD. I did suspect that the modem had a built-in ATA because my Panasonic phone does not have one. If I try to go with Vonage or another service like that, assuming I can drop my telephone service with AT&T (which might not be possible), I'll face another problem, no doubt. I don't know that routers will accept bonded pair inputs. I'll have to check into that. I think AT&T has me by the proverbial short hairs.....