old thread but it didn't seem to be resolved that yes QUITE in-fact there are two electronic systems in the key fob; one for the remote functions and one for the immobilizer.

The immobilizer doesn't use battery, probably similar to RFID or uses a crystal transmitter system of some type to report back a unique identifier code that must match the one in the car.

i've used my key with no battery, it will start the car. I've also tried to start the car when the key fob fell apart and it won't start, the guts are quite required.

my dad's buick would start if the key was within about 6" of the ignition (his lock cylinder self-destructed and i removed all the pins; you could turn the lock with a screw driver, but it wouldn't start without the key near the ignition, but on the seat under the wheel was close enough)

like wedge described; my key was the same; too many drops broke some solder joints loose; it only worked when i squeezed 'just right'. after re-flowing a handful of the solder pin and re-attaching the main little capacitor in the dead center at the bottom the key snapped right back to life.

Lasted a year and then wigged out; re-soldered and back-to-life however the rechargeable battery is shot so i have a non-rechargeable in there while getting the new one ordered.