Are you certain this is a factory installed alarm?
When the alarm activates - does the horn honk, or is it a siren sounding?
Can you describe your Keyfob (remote)?
Because Chrysler used a transponder immobilizer system in most 2005 models. This is a chip in your key - so the vehicle can verify that is the key to be used in the vehicle. If the transponder doesn't recognize the key, spark and fuel are cut off in the BCM.
The keyfob is for keyless entry.
Also - the SECURITY lamp in the speedo cluster flashes when the security is enabled - not a standalone LED.
From the LED - trace the wiring under the dash to the brain of the unit.
It will have all the information on it - Manufacturer& Model number.
Reply with that information.
Typical "Dealer Options" are remote starts and alarms contracted out to third party car audio businesses for the dealer - who then marks up the price 300%... and not necessarily 'factory"
They tend to use entry-level, low cost alarms... like Code Alarm and Crimestopper.
Let me know what you find.