[ImperialCrown]

There probably is a fault code stored in the WCM if there is a key transponder fault. It could very well be SKIM key related.
They could also scan the CCN (cluster) and BCM for faults that are turning on the security lamp.

 

[ImperialCrown]

That could very well be. There are fault codes for RKE low battery. I know that a TSB was released in the past also that other transponders on your key ring (eg: Mobil Speedpass) in close proximity to the ign cylinder SKIM antenna could also set false codes and interfere with starting the car.

 

[ImperialCrown]

The problem may not be in the key. I believe that the fob battery just powers the lock/unlock transmitter. The security ID chip transponder for starting may be independent and passive and not require a battery for operation. A loop antenna in the column 'powers up' the chip inductively to read the ID.
Most fault codes for SKIM won't show on the EVIC or an OBDII code reader. Most readers only read PCM faults. You need a more specialized scan tool to read other modules,