I have a 1996 Maxima SE with 82,000 miles. After the engine gets cold, I have trouble starting the car. I’ll turn the key once or twice and the car will start and stall. The car will start after I step on the gas pedal a little. I have no problem when the car sits for 40 minutes to an hour.

Perhaps the fuel rail lost its residual pressure during the idle period. Next time the engine is cold, try this experiment. Turn the ignition key to ON, wait 15 seconds, then turn the key to START. This brief delay gives the fuel pump some time to build normal pressure. If your car starts readily and runs well after this brief delay, that will confirm this fuel pressure hypothesis.

If the brief delay does not enable the engine to start readily, the problem might be a faulty Engine Coolant Temperature Sensor or a bad Idle Air Control Valve - Auxiliary Air Control valve.

mine did the same thing
 

It would start then stall when cold. I had the car off and moved the throttle plate by hand, from under the hood. It felt like the plate was sticking very slightly going from fully closed to barely cracking open. I took off the intake ducting all the way to the throttle body and opened the plate to wide open. There was sticky residue on the leading edge of the plate (black carbon looking). I sprayed a rag with WD40 and wiped the plate clean and around the inside of the throttle body. Put it back together and it has started perfect since then. Took about 15 minutes. Hope this helps.