My car is an 1987 pontiac firebird with a lg4 motor. I have world product heads and a jet performance stage two quadrajet (not computer controlled). I have been having problems starting after short trips when the engine has not completly warmed up. For example last night I drove 5 min and parked and went into the grocery store for 10 minutes and came back out and the car would not start. It would just crank and crank battery is fine, just fully charged it the night before. Waited twenty minutes and tried again still just cranked and cranked. Had it towed home attemped to start it and it ran like crap for 10 seconds idling at 300 rpm and coughing and sputtering no throttle resposne then after 10 seconds ran fine. It starts fine at initial start up when it has sat over night but won't start after short trips. This is the second time it happened first time it happened towed it to a shop and they said it started fine the next day for them and they didn't want to spend my money chasing a problem, so the gave it back to me. Any ideas ignition issue, carb issue?

 

Here's a common problem with rebuilt Q-jets that you may want to check for:
On the bottom of center section of the carb there are plugs under the fuel jets. These are prone to get loose and drip a puddle of gas into the intake as the engine sits. This puddle will evaporate overnight. If the engine sits longer than 5 minutes (but not overnight) when you try to start it, it will be hoplessly flooded.
It's easy to check if this is happening. With the engine hot, wait 10 minutes and open the throttle plated fully and look thru them down at the floor of the manifold with a strong light. The accelerator pump will squirt 2 streams when you open the throttle, but it won't be enough for a "puddle" on the floor of the manifold.
Another way you can tell is to crank the engine with the pedal on the floor when it won't start, and it will cough to life.