It it turns off instantly then I don't think that P0352 is the main problem.
Even if half of the coil pack shuts off, you still have two cylinders firing. This would cause a sputtering to a gradual stop and at least a half-hearted try to restart.
This problem will need to be diagnosed right after the car quits and doesn't restart.
First check for spark and fuel.
A brief shot of carb or throttle body cleaner into the throttle body followed by a restart attempt may get an attempt out of the engine to start. It may fire up and stall. This would show that you have spark, but the injectors may be staying closed. (Use extreme caution when using any flammable aerosols around spark or heat).
To diagnose further may require a scan tool. Make sure that the scan tool can communicate with the PCM. Look at a scan tool sensor display under the sensor menu and see if you have a crank and/or cam sensor signal present while cranking.
If one (especially the crank sensor) signal is lost or missing, it could cause what you are experiencing without leaving behind a fault code. Many times after sitting and cooling, they will start.