Dash showing engine icon with a lock on it

This its really common for the ignition switch to fail on those cars and cause them not to start. It will set a code b2960 and or b3033 in the body control module. Especially when the outside temperature drops bellow 40 degrees. I would also check with the dealer because a lot of those switches were recalled. They use the same switches on the Saturn ion, Chevrolet Cobolt and hhr and possibly the Pontiac Solstice and Saturn Sky.I have replaced a ton of them on the Saturn Ions.