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That sounds to me like you just have a dead battery.
As you noted, the comfort module controls the alarm and immobilizer. The starter will not work when the alarm is actively sounding (and lights flashing) Typically anytime you hook up the battery the alarm will go off until you turn a key in the door.
Your symptoms don't seem representative of an alarm issue- since you have taken the module out of the starter circuit, the signal should go straight through to the starter from the ignition switch. It just sounds like a battery issue- check to make sure both your battery clamps are clean and tight, and the main ground at the body is clean and secure