Keybear,
I very much appreciate your frustration that something this simple isn't fixed. It's quite odd, but please keep in mind that nobody else knows what you did or didn't do or what Dillon did or didn't tell you to do until you relay it to us. It's so simple you may expect we should all assume you tried everything obvious. But when I part-timed in TV repair shops in college, you'd be surprised how many times I saw a trained, experienced technician spend fifteen minutes getting very frustrated at being unable to identify the cause of a dead device before finally realizing he'd never plugged it into an outlet. Call it brain "gas" or whatever, it happens to everyone once in awhile, and the simple questions are just to eliminate those possibilities and not to make you feel like an idiot. So please have patience with them, taking solice in the fact that even a trained technician can miss the obvious.
In this instance it seems to me that you are down to one of a few possibilities. Since several units did not work, and since you tried batteries that were known to successfully power other devices, it isn't going to be something you failed to do correctly. Period. The explanation is going, therefore, to be academic to us. Dillon may have got a bad lot of buzzers. An old fashioned electromechanical buzzer doesn't care about polarity, but they aren't used much these days because they draw a lot of current. I just happened to get a replacement buzzer from Dillon earlier this year, and the familiar little white cube is gone and a short cylindrical piezoelectric sounder with built-in transistor drive oscillator has replaced it. These do require the polarity be correct, and if they purchased a lot with the colored wires reversed, that would stop it. I once found a name-brand 9V battery with its + and - snap terminals terminals reversed and therefore providing the wrong voltage polarity to anything you snapped it into. Murphy's law is alive and well.
In the case of a piezo electric transducer, it will not work and I though might be damaged if the polarity is wrong, though I wouldn't expect anything less than 3 volts in reverse polarity to damage the conventional bipolar transistors used in these things. So, I decided to test that on my working unit just to see what happened. It did no harm. So I think you can try that safely if you haven't already (I forget if I read that you did).
But wrong polarity its not the only thing that can jam these little guys up. They can be damped out of oscillation by the glue some use to attach them to their mounts if it smeared out over the surface. If that happened, the buzzer should make a click sound when you close the switch, though you may have trouble hearing it over the click of the switch itself. If they are soldered to their lead wires, using a little too high temperature solder or too hot soldering iron can cause the deposited silver that comprises the contact surface to flake off the piezoceramic material's surface, breaking the connection. If there is transistor damage, that would require a multi-meter with a diode test function to verify the circuit is open in both directions. If you know somebody with one, you can try that, but the exercise is really academic.
I am dismayed that Dillon doesn't seem to have tested your returns to confirm your results. I suspect the way their warranty service folk are trained is not to mess around with parts, but just to send another one, and that solves the problem 99.99% of the time. But if they got a bad lot of components, that doesn't help. On the other hand, if they got a bad lot of components, you'd figure they'd have had similar complaints from others by now and had a correction in place. So I don't really know what the deal is here.
While it would be interesting to know the exact nature of the problem, the practical thing for you to do at this point is to write snail mail to the president of the company and ask him to please, please put a battery into one of these things, test that it actually buzzes and, if so, to send it to you and to please include the battery he used just to be sure there is no possible confusion. You can copy the salient parts of this post to him if you wish, as I am an electrical engineer by training and the fact that I can see ways in which they could have a component problem may stir them to try the test and to check other units in stock. They may be getting the soldering work done by an assembly house who is supplying the components and who isn't testing properly. The president should want to know that if it's so.