This is an instance where having a real ohm meter, one with the leads, will help. A mechanical mod is real simple, the electricity goes from the top of the battery, through the stuff in the top cap, into the atty through the center pin, through the coil, back to the top cap through the outside of the screw on the bottom of the atty, into the tube, into the switch on the bottom, through the switch, and back into the battery. At some point in the circuit something is blocking the electricity. You need to use the ohm meter to insure the electricity is flowing through all the connections.
Try it with the battery in and measure the voltage were the atty screws in, this should be close to what the battery has. If you get voltage here the problem is with the atty or the connection to it. If you don't have voltage take the battery out and test the resistance at each of the connections. Eliminate ones that work until you find the one that fails, fix it, and your problem should be fixed.
If it is a good shop they will help you to find the problem.
Good luck. I once spent an hour finding out that the button on my nemesis was not touching the negative terminal of the battery because the battery wrap was too big.