Aftermarket headunit? That's the only reason I could see a dealer not wanting to touch it..... If it's stock, then you're getting pushed around by your dealer. I'd report them to Mazda.
It sounds like a fuse to me. It's obviously not a connection problem. I'd check all the fuses with a multimeter. FYI, they all have test points on each side of the amperage markings. Run your probes down the line and you should have the whole panel done in 60 seconds. Check the ones under the hood too. If you don't find anything, remove the headunit and test for +12V battery and +12V ignition power in the harness. If you don't have power, then it certainly has to be a fuse somewhere. If you have both +12V power sources and ground, then the headunit should power on no ifs ands or buts. If it doesn't, it's toast.
Last edited by firebirdude; 06-24-2012 at 12:52 PM.