Having some issues with my mazda3 2007. Up until now I have had no issues with the car. Saturday was sitting in a parking lot waiting for it to clear had the key turned for 20-30 mins to listen to the radio. Went to start it and it would not start (dash board lights on). Jumped it and started no issue. Drove it for 45 min and it started the next morning no issue. Drove Sunday from LA to Las Vegas turning car on and off along the way no issue. Monday drove the car first thing in the mornin no issue. Had the battery tested that afternoon and they suggested I replace it (4-5 years old). Autozone installed, I watched all looked good and I was on my merry way. Parked the car in my garage and it sat until Wed morning. Went to leave and it would not start. No lights, no turn over, no clicking. Car was jump started that afternoon and driven back to autozone about 2 miles away and it died right as we pulled in. Power steering went out and then car completely shut down. Battery was charged put back in and died right away. Autozone replaced the new battery claiming it was bad and suggested coming back in a couple days to have the alternator tested. Car driven home no issue. 2 hours later started the car drove 3 blocks forgot something and went back to the house for less than 5 min came out and the car would not start. No lights, no turn over, no clicking. We took the battery out and had it tested and the battery still had a charge. Removed the alternator had it tested and was told it was good. Check the negative ground off the battery and it was tight, no corrosion could be seen. Checked the fuses relating to the car starting and did not find anything faulty. Cleaned the connectors on the battery with basking soda & water.

Can't seem to locate the issue. Suggestions?