I'm with JT on this one. You said in your other post that when you cycled the pump a few times (turning the key to the accessory level and back to off) the car would crank up. You also said that once you got it cranked and cut it off it would crank right up.
This has, to me anyway, fuel pump written all over it. It sounds like you are not getting enough pressure on the lines on a cold start. The reason it cranks right up after running for a bit is because there is still pressure in the fuel lines, if I'm not mistaken.
one question: The new fuel-pump isn't doing anything for you, right? From reading this I wasn't sure if you have installed it or not.
Also....what is your battery voltage? I'm sure you've prolly checked this, but you never know.