Putting aside for the moment the ethical issues (for all I know you have permission), and assuming you currently have a combination modem+router, you can't actually turn it into just a router. A standalone router always exposes a WAN port (which of course is connected to the modem), but a combo device establishes the connection between the modem and router INTERNALLY. And without an exposed WAN port, there's no way to use the device purely as a router!
That’s the downside of combining components. While it’s convenient, reduces the footprint, and minimizes the complexity of the setup from the ISP’s perspective, it also hinders your ability to reuse it for new purposes. You’re basically stuck.
Despite all that, I’m not sure it even matters since I'm assuming your neighbor is using wireless, and that what you really want to do is establish a wireless bridge (aka WISP (wireless ISP)) from your wireless router to theirs. If that's the case, and if your modem+router supported wireless bridging, it would be possible. Unfortunately, it's extremely unlikely that AT&T device would actually support it.
Bottom line, the chances you can access your neighbor's wireless w/ your current modem+router is next to nil. You'd have to consider another router, one without a modem, and which supported wireless bridging. Some routers do have this feature, esp. any that support dd-wrt third party firmware.