Does it happen every time? It sounds like it could be a vacuum leak or a fuel pressure regulator. Fuel pressure regulator usually is engine temperature dependent. When mine went it would act as you describe when I tried to start it warm (ie after a long drive then it only sat for 30 min) but if I let it sit for a few hours it was normally ok.

When the hose coming from my pcv valve split(vacuum leak) no matter what the temperature of the engine was it wouldn't stay running unless I kept the rpms at 1200 or higher.

When the engine shuts off the check engine light and battery light always comes on, that doesn't indicate a problem at all. Only if those lights are on or flashing while the engine is running.