Hey, I've got the Mazda6 shop manual on my computer, I've found the whole section on trouble shooting the climate controls/hazard light control wiring (the 2 plugs that go into the back of that part of the dash).
I cannot seem to find a way to post up the PDF pages to show you the tables, but basically if you have some multi-meter skills you can measure the voltages on each of the wires to see what section is causing you trouble, and it'll also tell you if the wiring to the climate controls is the issue, or the circuit board/climate control itself.
PM me your email address and I can hopefully find a way to email you the pages or even the whole shop manual.
I cannot seem to find a way to post up the PDF pages to show you the tables, but basically if you have some multi-meter skills you can measure the voltages on each of the wires to see what section is causing you trouble, and it'll also tell you if the wiring to the climate controls is the issue, or the circuit board/climate control itself.
PM me your email address and I can hopefully find a way to email you the pages or even the whole shop manual.