My 2004 Scion Xb won't start. Bought a new battery for it. Essentially, car was idling rough for a few days. Then it died at a traffic light. No electric, no nothing. Upon replacing the battery, all the lights and electric are working. I managed to get the car to start when I first hooked up the battery, but it was still idling rough. I turned the car off the tighten connections. After that, the car wouldn't start. When I put the key in the ignition, the lights all work. When I turn the key, the car does not start and all the lights (except the battery light) go out. When I remove the key, the lights go back to normal.

Any ideas?