But is it STILL showing 12.6 volts? The battery light GENERALLY and almost ALWAYS means that the alternator is not charging. There are many reasons for it not to start OTHER than a weak battery, but the fact you saw the battery light then it quit running still makes me question the current state of charge in the battery.

Apart from the alternator/battery, a car that quits running and THEN won't start, that is, won't engage the starter, is usually the RCM.

If the car won't start, do the standard test: Leave key at "ON" and wait 30 seconds. If the engine fan warps up to high speed (you WILL hear it) , then the RCM is probably at fault - the ECM is not powered up but the FCM is, hence the high speed fan with key "ON".