I'm posting this trying to help a friend. '04 w/ 80k miles.
He just replaced the battery at the dealership after having it towed there due to flooding.
It started at the dealership, and while driving a few miles down the road, the engine died. It started and then died three more times.
He contacted the dealership and they said that he needs to drive it for ~50 miles for the ecu to get used to the new battery. I've never heard of that before but I'm not familiar with rotaries or the mazda setup but am learning as I go.
So he got in the car, went to crank it over and everything shut off. He pulled the key out, and the lights started flickering on and off, and the gauges were bouncing back and forth, with the key out of the ignition. I would say it was a loose connection somewhere. We are going to go look/mess with it today, and I thought I'd see what you guys had to say.
What should we start looking at?

 

Check the connections. My car was doing something similar and ended up the positive cable looked like it was tightened down onto the battery but wasn't. I removed both, tightened them down, and it worked.

Also, check for corrosion around the battery posts and the cables themselves. IIRC the cables like to corrode on these cars as well and that could be causing it.