OK, there is a lot of incorrect information in this thread. For the sake of people reading this in the future, I'm going to correct the major points.
This does nothing. The fuel quantity injected is defined in its own table in the tune, and has nothing to do with throttle position. On my LB7 I verified this by flooring the truck before cranking, and leaving my foot on the floor. Not only did it start just like normal, but it sat there and idled even though I still had it floored. I had to take my foot all the way off the throttle before it started listening to my input.
Oh dear lord NO! The Duramax handles this a little better than the 6.2 & 6.5 of old (which would usually bend connecting rods immediately), but you can still screw up your engine with the violent pre-ignition. The only thing worse is the people who pour liquid diesel into the intake
The injectors fire only when the fuel rail pressure is 10 MPa or higher. If the CP3 manages to compress air to 10 MPa (~1500 PSI), the injectors start firing. However, that is unlikely, as it is very difficult to compress air to 10 MPa. Odds are your fuel rails still had a bunch of fuel in them.
Finally, several people mentioned cracking injector lines. This is unnecessary on common rail engines, and can be quite dangerous. At the pressures the common rail system operates at, it can penetrate your skin, which can be fatal in some cases. Additionally, it can damage the sealing surface of the injector lines or fuel rail, causing them to leak permanently. The air in the lines will be compressed to virtually no volume once fuel reaches the CP3, then be purged out the injectors as soon as the rail reaches 10 MPa. Cracking the injector lines does more harm than good. I've never had to crack the lines to get a Duramax to start, and I've done 3 injector jobs.
Hopefully this will help someone searching in the future get the correct info.
Odds are you have an air leak prior to the CP3. When you prime it, the fuel filter and lines are pressurized, preventing air from leaking in. Once the truck runs, it starts to draw the pressure down, eventually drawing a slight vacuum (which is how it gets fuel from the tank). If there is a leak, even an extremely small one, it will pull air in, and die.
To determine if this is the case, start the truck, and keep priming while it idles. If it keeps running as long as you pump and dies when you stop, then you almost certainly have a leak. The most likely candidates are a bad water in fuel sensor or bleeder screw. Usually, these will drip a bit when you've primed it as hard as you can, so hopefully you can find the leak that way.