I realize this is an old post and I sure hope you've got this problem worked out. For the sake of making sure this information's available to the next person...
Connected to the back of each lock cylinder there is a small switch. You can disarm the alarm, using the key, via any of these locks. The switch is a mechanical switch and as such they do wear out; The driver's door's switch is typically the first to go followed by the trunk.
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