New Battery now idle dying after start

[katiscrlet]

The battery on my 2004 G35 (35K miles) died today. I took it to the dealership to have the battery replaced and check the alternator out as ok, but once I got home and tried to start it again the car idles up then immediately dies. If I give it a little gas it starts up and is fine, but only if I give it a little gas. I have never had this problem before the battery dying today. This is not making for a very good Mother's Day weekend. Any suggestions??