How much does it cost for incompetent service?
Ha...they sent you a bill for "no service" at all?
The fact that they didn't even connect the service initially would have me giving them a piece of my mind....
Call them back and demand an additional refund for all your trouble, essentially YOU did THEIR job for them.
Tell them politely that if they do not wish to compensate you for all the trouble and inconvenience you will be contacting your public utility commission, the NM Attorney General, and the BBB. I can promise you they will send you a check.