You also need to make sure the throttle blade is not real dirty and has any carbon build up on it as that will also do it. And thats because the IAC (Idle Air Control) motor is programmed in the PCM to go to a certain amount of steps at a certain temp and it also needs the extra air that gets around the throttle blade or it will stall and may not start just as you said. The PCM is not smart enough to know that it needs to open more because the throttle blades are dirty and not letting enough air by them. Its made so the IAC just fine tunes the idle speed but when at its setting it must have the air around the throttle blades to have the right idle. The IAC will adjust some but not fast enough to start the car or keep it from a stall when you let off the gas. Its like say the IAC motor is set for 35 steps when it sees the eng at 65 degrees. So now when you turn the key on the PCM sees the temp of 65 and sets the IAC at 35 steps but if that extra air is not getting around the throttle blades the eng will not start or will barely start and stall. Now if you put your foot 1/4 to 1/2 way down the eng will start since you open the throttle and if you bring the rpms down slowly and take say 60 seconds to do it you will slowly see the IAC steps go from the 35 steps it is set at by the PCM for that eng temp up slowly to about 60 or 70 steps and then you will see the eng idle like it should. But if you drive down the road at part throttle while you drive the PCM will adjust the AIC back to 35 steps where it is programmed at that eng temp and the eng may die when you let off the gas and come to a stop. Step on the gas and the eng will start and do the same thing.
Now if you pull the throttle body and I use a tooth brush to clean all the carbon off the throttle blades you should see when you put it back together it will start and idle fine at the 35 steps the PCM has the IAC set at. Remember the IAC steps are higher on a colder eng as at 20 degrees it may be at 70 steps but if the throttle body is to dirty and blocking the air made to go around the blades it will still die. And on a completely warm eng at idle with all acc's off the IAC may only be set at 20 steps. Course it can change if you modify the minimum throttle blade setting which you should never have too. But definetly make sure the throttle body blades are clean. And as was said if the battery goes to low the PCM can forget where the IAC is set and needs to relearn that also. Good luck , Ron