cylinder misfire

I have a 2003 ml 320. check engine light came on and car stopped running. The car will turn over but run for about a minute then shutsdown. When I turn on the car and removed the positve battery cable from battery the car shutdown immediately. I believe I have a bad alternator. when I hook up the cumputer to the car i get multiple cylinder misfires. I get cylinder 6, cylinder 5and cylinder 4 are misfiring. could a bad alternator cause the misfire reading?