I have a 30 year old shed 50' from my house that was wired with two lites and three outlets. They worked had electricity when I moved in 6 months ago. I suspect the the underground cable was somehow severed when the gas co dug a trench in my backyard in August. They deny it. Is there any way a break in the line can be located and repaired. I checked the circuit breaker panel and they are all on.had electricity
The break in the wire can be confirmed by placing a voltage on one end of the pair then measuring for it on the other end.
If you know you have voltage on one end then simply having lack of voltage on the other end is proof positive.
If you have 3 wires to work with, then you can use a 12 Volt battery like from a car, then put it across pairs of wires, using a multimeter on the other end, to determine precisely which wire is broken.
If a trenching machine is responsible then it is most likely they all have been cut.
The precise location of the break can be located by using a time-domain reflectometer.
If the gas company came out and dug and you haven't had power ever since then their denials mean nothing until they come out and prove that they did not cause it.
I wouldn't let them off the hook until they send out technicians to prove their denial.
I would go so far as to tell them you think there is live electricity right near where they dug for the gas pipe. See if that will get them off the dime.