The only way to know for sure would be to either ship your unit in to be tested at the factory or (much chealer) test another Humminbird unit on your boat and your unit on their boat. Our Customer Resource folks were right: almost any Humminbird unit will work on your transducer. Try testing another Matrix, 100, 300 or 700 series unit on your boat as these will all just plug right onto the same mount like your Matrix 27 does. You could also test it with a Piranha, PiranhaMax (PMax), 900 or 1100 series units as well but would have to take the power and transducer cables out of the unit mount base to do so. If someone else's unit works on your boat (or if your unit does not working on their boat), than the problem is in your unit. If their unit does not work on your boat (or your unit does work on their boat) , than the problem is the transducer or the transducer mounting.
If the problem is with your transducer there are some things you can check. You did not state where your transducer was mounted so I don't know what to suggest here.