Here's the deal : The fob has only 2 functions when it comes to starting the car
1. Physically turn the switch to engage the starter.
2. it has a non-powered chip in it that is excited by the key ring to generate and broadcast a code sequence that is received by the same ring and delivered to the SKREEM. The SKREEM then decides if you are allowed to start the engine.

As far as locking/unlocking, that is done by the POWERED circuitry in the fob, it sends a code sequence to the HomeLink module ( up with the dome light ), and then it communicates with the locking pump in the trunk to lock or unlock the doors.

What you have does sound like the first stages of a full blown case of SKREEM-itis to me.