Code P0687, cranks but will not start?

After stopping at a store, I got in the car to leave but there wasn't any power. I checked under the hood to find a loose battery cable. Tightened it and it started right up. After driving out of the store parking lot, the car suddenly shut off on me with the battery light on the dash illuminating. I tried to start it again, but it would just crank. However, when trying to start the car in cranking position, it seemed as if the cranking position would stick, continue, unless I turned the key off. I then shut the car off and called for a tow truck but after waiting two hours and no tow truck, I decided to try and start the car again. This time it started right up and I was able to drive it two miles to get home. The next day I replaced the battery after having it checked. The AutoZone said it didn't have enough cranking power after they charged it about 12 hours. I installed the new battery, and it still won't start. I removed the alternator and also has it checked at AutoZone. They said it was fine, so I reinstalled it. Car still won't start but does crank. I used a neighbors obd11 scan tool and received the code P0687. Any help would be appreciated.