Could you explain what you mean by "wall box"? Do you mean the NIU or the phone jack? Why do you assume the problem is there?
In general, any phone wiring past D-mark(point where Cox wiring ends, and yours begins) is customer responsibility unless you have a line protection plan of some type. It would be on your bill or you can ask if you have it before you make the appointment.There are some exceptions to this rule, to allow flexibility for the technician in the field, but thats the rule of thumb.
Where the d-mark is differs from house to house. If you have a phone modem, then it would be where the cable wiring is connected to the electrical ground. If its NIU (see above) then it would be where the phone wiring attaches to your punch block, or is physically in your house.