Why over think the starting and stalling? Your other post points directly to a CPS. Its not good to be driving around with a broken PCM connector. How did it break? Is it still able to make good connection? Maybe you should check this out and if it looks good then replace the Crank Position Sensor. Which by the way shoulndt run you any more than 50-60 bucks. Make sure you get an ac-delco replacement. It is an easy job thanks to our writup in tips and maintenance. The writup is for a series II 3800, but I dont think the series III is much different (if any).
Crankshaft Position Sensor Replacement '97-'03