to NICO!!
I'm not sure what the weather is like in your part of the world, but it's possible that the engine is flooded. In cold temperatures, the ECU sends a particularly heavy hit of fuel to the injectors before a cold start. Think of a reverse old-school choke... but instead of enriching the fuel mixture by cutting air, they're doing it with more fuel. If the car is started in cold weather, moved a little, then shut off - all of that extra fuel can wash the oil off of the cylinder rings, causing low or no compression. The ECU has a feature to bypass the enrichment at startup that involves holding the gas pedal to the floor during starting. Typically you'd floor it, turn the key, and don't stop until it either starts or the battery needs to be recharged. We typically see these issues at about 40F (4C).
As others have mentioned, I'd check fuel pressure... a super fast bleed down after shutting the car off could indicate that an injector is leaking in to the engine, and cause a similar issue.