05 corolla - I have changed out coil - the same code comes back- I switched out the coil with all spark plugs cleared computer code-the car worked fine then started to stall out - looked up the code and it was the same code p0353 coil C- is this a corolla problem -bad harness coil No. 3(C) or a computer reading something wrong-

Since you've changed the coil, thoroughly inspect the harness and connections at both the coil and the ECM.
It sounds like you will need an ECM.