2009 Toyota Corolla Stalling out

I did check the Lemon laws for NYS, where I live and purchased the vehicle, after getting the call from the dealer saying they had no ideas about what the actual problem is. They have 4 attempts in this state before the Lemon Law can be employed…We are one down. And thanks to your suggestion, I did file a complaint with the NHTSA, so they now have a complete record of it, too. The 2009 Corollas are a new design, but I do not know if the engine and electronic systems are a new generation or not.
Thanks for your help, Monique