I'm having the same exact problem with an 06 crossfire limited, not the supercharged model. My car has 9,200 original miles on it and when I had sat in the car idling for about ten minutes it died like it ran out of gas. It would crank over like mad but wouldnt start or stay running without dusting it with starting fluid and then it would run great for about 5vseconds then die out again. I believe I'm having a fuel problem. I changed out battery with a high cca rated battery and replaced the crank and camshaft sensors. I Al's put a new fuel pump and German fuel filter. Any ideas? By the way the connectors are online with napa I believe.