Cadillac Repair: Assuming an electrical problem, starter relay, electrical problem

Question
QUESTION: I have a 1999 Escalade and it has two alarms one is the "onStar" which is factory installed. I don't know what the other is.  However, the car will run well but as soon as it is shut off it will not start up again but there doesn't seem to be any problem with the battery.  The horn will blow, the windows work.  I just can't get the car to start.  It does not make a sound.  The the next day we go out and it starts right up.  It seems to be getting progressive worse now because some days it will not start even after waiting for a few days.  Do you think it is just a matter of removing the alarm system? or do we have a major problem?

ANSWER: If the other alarm system was NOT installed by the manufacturer, Remove it.

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QUESTION: Is there anything else we should be concerned with as it relates to the car failing to start without warning?

Answer
When you say engine won't start, Do you mean that when you turn the ignition key to the start position you hear NOTHING AT ALL ?.

Remove the aftermarket system and restore the factory system and let me know what happens. It is possible that if you hear NOTHING when you try and start the engine that the fault may be in the PASS-KEY theft system, the starter relay or the starter itself.