Given all the troubleshooting, I'd say the cable is fine and its their box(es). I'd see about swapping them, or calling out a tech and fighting the install fee; its not your fault they gave you crap boxes.
Another way to test; move your modem and router to the TV's cable. If internet works there, you KNOW your infrastructure is good and its their boxes. (and therefore they shouldnt charge you to come swap the boxes/install them)
Another way to test; move your modem and router to the TV's cable. If internet works there, you KNOW your infrastructure is good and its their boxes. (and therefore they shouldnt charge you to come swap the boxes/install them)