When I had the ignition off a few months ago I noticed a pickup coil. Does that read a chip in the key at all? Assuming it has one, could it be the chip in the key is suspect? That might explain why putting the key in doesn't override the alarm?

The coil is a passive device that excites the fob and the fob sends a code that is picked up by the RF reciever - the post 99 models had this coil fitted to allow easy sync of the keys - put key in ignition , turn it on, the coil excites the fob, the fob transmits to the RF Rec. the BeCM checks the code from the RF rec. and if it is correct, it sends a new rolling set of codes to the fob and the car starts.