What causes a crank but no start in 2009 Toyota Corolla

Hi, first of all stop checking for diagnostic trouble codes if the car isn't starting. If the car isn't starting, nothing can run and indicate failure in the first place. A check for a crank no start should be checking for presence of spark and fuel and air to the engine. Also, it's important to make sure no antitheft devices are preventing starting. This can very well be testing done hands on manually checking components - not with computers. Since you stated especially cold and rainy temperatures influence poor starting, I would lean towards possible coil and coil boot issues allowing moisture into the spark plugs preventing cylinder spark. It's all a guess; get some help from a tech near you. https://repairpal.com/auto-repair-near-me#&zipCode=