Unknown Issue but Possibly Charging System

After sitting for almost two months due to bad brake master cylinder that issue was fixed and all is good with brakes. However within one week while driving to work the "Check Charging System" warning came on the dash. Then went off then back on and so on. Car still would run and all and if I turned off A/C and stereo the warning would instantly go off. After the 2nd day of this the car even with the A/C and stereo off sounded the warning again and as I was breaking for a stop light the car sputtered, stalled, and died (dead as a door nail with absolutely no power including hazards).. It had to be jumped three times to get home (less than two miles away). OK so battery has been replaced and new alternator. Car was jumped after new alternator was installed and was let to run a while with A/C, stereo, etc and never died. We took it for a drive and after getting up to 45 for a few blocks it again tried to sputter out and die as before. My question is can this be related to the charging system and or brain? Or a separate unrelated issue that just so happens to be presenting itself at the same time? I have also been told letting the battery go totally dead and the car setting for a while can mess up the brain? Any suggestions would be great. We are doing all we can DIY due to lack of funds... PS. When the car is beginning to bog down and sputter the A/C stops working. Not the blower just the cold air...