Would a dead battery throw a Check Engine light.
You turned on the ignition, the computer gave you time to get it running and the computer is NOT at this time receiving pulses from the engine counter, Thus it thinks the engine is not running, (Which of course it is not) so something MUST be wrong with the engine.
On an OBD 1 it would be sending, if I Recall correctly 8 8 8 as the trouble code (Means, Engine is not running.. Ok so they have a much fancier translation but it means.. Engine not running).
Alas this is the kind of issue I am better at with hands, and a test light, ON scene.