Since you ask, I will try to give a different perspective.
This is both an easy and a hard question. The first obvious answer is that yes you should get a refund for a defective product. After that the answer gets complicated. If you have a history with this company they will honor your request for goodwill.
I have little sympathy for those who think diagnostics should be free. I do not know what you were charged for but I can tell you that the cost of processing an invoice is probably equal to an hour labor in most shops. I can not imagine charging $79 to diagnose a waterpump noise. I can tell you that estimates are guesses in many cases. It requires considerable disassembly to make a real repair sheet. We often estimate high and then bill for what we find. It has been years since I accepted the burden of all the potential risks in every job. With thirty years experience I still miss a part in a significant number of parts estimates.
What you must understand is that in many cases a proper diagnosis can require half the work of the whole repair. Usually in the interests of efficiency a calculated risk is taken which is then covered when doing the work.
I will give you an example: a car comes in with a driveability problem. With thousands of dollars of the best equiptment I can only hypothesize that the problem is the engine management system controller. There is absolutely no way to do this diagnosing absolutely. The controller can not be tested in the field by anyone! I make the call. Now a couple things can happen. The most common is that I buy a used controller as a test case and if I am right the customer gets a great deal. If I am wrong I put the controller on the shelf and the next car I use it for the diagnostics. But, we didn't talk about the estimate. Before I tested I told the customer that I would be charging them two hours labor for the diagnostic. At that point I have had more than one customer want to get their own controller and maybe even do the simple installation. At that point I inform the customer that they have paid me for my time and they only get the warrantee with my doing the work and providing the part as I will then be accepting the risk of my diagnosis as I won't be charging them if I am wrong (for the part not the diagnosis). I will also then have to do more work to find where my testing didn't add up.
BTW in cases where there is no used controller available (or used is not an option such as late model engine controllers that marry the chassis number) I will spend probably double the standard diagnostic time before making the call. I call it diagnostic risk. The testing necessary for calling the 200 dollar used is much less than a 1600 dollar new Porsche one (been there many times).
I did say that any good businessman would return your money, didn't I. But let me warn you that business is run off doing the repairs not writing estimates. The amount of diagnostic risk a business will take for you depends on your presence as a customer.
Bosch Master, ASE Master, L1
33 years MB technician