Since you said AT&T router, Do you have a service that you are supplied their router? If so as long as you have WIFI turned on your phone it should at least find your router and whoever set it up be it you ot AT&T you need to have a passphrase on it that someone would have set up, Then your phone would at least find it, Once you and you select it, it is going to ask you for a password - enter the same one and you should be hooked up to WIFI and from there you can back up tp iCloud as long as you know the proper way to do it ( the steps) once you plug in to the charger.