Hey Nightflight, thanks for your question.
This car likey has a factory alarm system installed, which works with a hood switch, try to find it on the vehicle somewhere (not on hood) and depress it. This might get you started. If not, and the alarm has somehow been tripped,and needs some attention
Try this to remedy it:
key into ignition- turn to ON- turn back off- push little button behind blue alarm light by your leg area 3xyou will hear 2 soft horn beeps confirming programming.
Let me know how it goes
Thank you for responding back, but since we have limited time before I have to leave town, I tried buying a new battery. It worked.
FYI, no hood switch, no blue light and button.
I'm glad you got her going, I assumed the battery was strong from your post and failed to mention that the procedure was only for Mazda 3's that have a Karr alarm system installed from the factory.
Thanks for your question.