That's smoking good voltage from a battery installed in a CTS with the ignition on and engine off, like a battery with no load at all on it. Check battery cable connections and don't trust that reading without a formal test. I didn't know a reading that high connected up was even possible from a typical car battery. I'm in agreement with the previous response as your symptom is characteristic of a bad battery, good enough to power up the dash, but no guts to start. Check your oil level also, a seized motor and or bad starter tends cause this kind of symptom, but then neither of those situations would leave a battery with a 13.7 v reading after the first start attempt.