Just went through this with our Toyota. The tech checked for a short (nope), a good ground wire from the battery (good), and the regulator and alternator (BAD DIODE in alternator). Replaced the alternator. He said a battery, even if new, can be damaged by a full discharge, and to see how it worked out over the next week or so, as it may need replacing as well. Good luck!
2003 Firemist Red/grey leather SL 500
2015 Palladium Silver/black mbtex GLK 350
1987 Smoke Silver/burgundy mbtex 300E Sportline (SOLD)
Click to see 87 300E