Sean asked me to chime in. Not sure if I can really add a whole lot to what's been already said here but I'll try.
All I can really offer is a copy of this document which takes you through the steps of diagnosing a P0068. One interesting thing is that as a diagnostic aid, it says to check the cam sensor circuit for shorts to ground. Unfortunately, some require that the engine be running and need a high end scan tool, probably a Tech 2.
The way you describe the problem, it sounds like a gross air leak somewhere. Could you post a video of when you try and start it? Do you have a buddy that can help you? If so, have him/her keep trying to start it and while it's running for those 2-3 seconds, spray carb cleaner around the intake and vacuum hoses and see if it runs longer. Another thing you could try is blowing smoke into it, like in this video. Maybe tape up the throttle body and use the brake booster hose for the smoke.
https://www.youtube.com/watch?v=zMok2y05jNE