Our 2010 Mazda 3 with a standard tranny has done this twice. When it was parked with just the radio running for about 10 minutes, it would not start. All the dash lights flashed off and on. The starter would not engage. The battery is fully charged , and all connections are clean and tight. The car always starts otherwise. My dealer doesn't know what could be done. I asked if there was a relay that might be sticking, and if they could do any testing or had had similar issues. They said they didn't have any testing they could do, unless it happened at their shop. This only happens when it has been parked with the radio running, in accessory mode.
Any ideas.