Shut off while driving and will not start?

Our daughter's car listed above will not stay running. It threw a code that said one of the spark plugs was bad. This was several months ago. It had been running rough. Replaced those and it helped it but was still running rough. On her way home from college, she came to a stop sign off a highway where it was running fine. Started idling rough when she stopped. She started out onto another highway so accelerating to get up to speed and it started sputtering. Soon she hit a hill and accelerating up that made it even worse. The car shut off along with all power at the top of the hill. She had to coast to the side of the road and the car would not restart. Had to have it towed from a remote highway in the middle of KS. Since having it home, we have replaced the fuel filter and fuel pump, exhaust system has a hole in it so we have disconnected that, so it isn't an issue, we replaced all four spark plugs and wires and housing unit, two of the plugs had gone bad in a couple months, looked like faulty product, checked oil and coolant, all looks good. The car now will "start" roughly as long as the key is turned forward and you are giving it gas. When you let go of the key and gas pedal, it shuts off. :( Any ideas on what to check next. Until these last couple months the car has been really good and a strong car. We had the A/C compressor replaced last summer. Our daughter saved up and paid cash for this car as a high school senior. Now as a college student without much money, she hopes to limp it through to last her a couple more years. Thanks for any and all help and suggestions!