I've been having this problem on my 02 Silverado for about 10 years. A few years ago, I bypassed the ignition cylinder by hard wiring in some resistors,and "teaching" them to the BCM; this worked fine for about 2 years until the unit would randomly drop the code. I thought I had the hot lick by getting another BCM off eBay for $20 shipped. Installed the new BCM, and relearned via the 10 min. procedure 5x to no avail- no start. I was talking to a high performance friend and he found the stupidest fix I could ever dream of on a software website. The post included the following procedure: Get in the car, shut the door, ignition on, ignition off, window down, window up, lock, unlock... The blasted thing started immediately! I was flabbergasted to say the least.
On a sidebar: I am playing with a 2002 3800 Series II v6 transplant into my 85 Pontiac Bonneville. The engine came from an 02 Firebird equipped with what I now know as Passkey 2 or 3 (resistor in key, to BCM, to PCM). I have now learned that the PCM also shuts off the injectors as well as the fuel pump. This is done via the Fuel Enable circuit to the PCM. It can be duplicated with a 5v 50hz sine wave on Passlock systems which is probably all the newrockies device does. My v6 PCM did not have the option to ignore the VATS or Fuel Enable circuit, so I had to wire in the BCM. Unplugging it while running will fool the PCM until permanent pwored is removed, at which point, the signal needs to be resent.