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P1514 GMC: Code Meaning, Causes, Symptoms, & Tech Notes (engine-codes.com)
The 1514 code is a throttle issue. The 3.8 is a "Drive By Wire" system. Which means, the throttle is controlled electronically, Not by a mechanical cable. This means the system has a few sensors.
No, running out of gas isn't going to throw the Security light. If the Security light comes on at all. there is a VATS issue. A VATS issue will create the symptoms y'all are experiencing. The VATS system has 3 stages. 1st stage is a light on but will still start. If nothing is done to fix the issue, it can go into the 2nd stage, which is an intermittent start/no start. The 3rd and fibal is a flat out no start....... not even an engine cranking. This one MUST repair the VATS issue. Which is usually a worn out Chip in the ignition key. A new "chipped" key is required. Or do a VATS bypass.