When it starts shine a light down the carbs throat and see if you see fuel dripping out of the boosters. If so it's flooding likely due to trash in the needle and seat. Snatch out a few spark plugs and see if they are wet or have a heavy fuel scent to them, if so that points towards flooding.
Check it for vacuum leaks, a major vacuum leak will also cause it not to idle.
Which Quadrajet are you using? Is it the type that has the electrical plugs on it? And by the way, the Quadrajet is hands down the best street carb made, but it's the same as all other carbs, when they got a problem they don't work correctly. Lastly, are you using a adapter plate? If so what type?