If the theft light is flashing rapidly then it is the anti-theft system shutting down the fuel and ignition systems. This occurs when the computer does not receive the correct signal from the transponder key (your key has a chip that sends out a signal that the key cylinder pick up via an antenna in the cylinder.) when the computer does receive a good single the theft light will light up and stay lit till the engine starts.
I installed a remote starter in my x (98 sport shoc) last fall and ran I into this same problem. The starter would crank but no start, and the theft would blink rapidly. this was because there was no key in the cylinder. To get the starter to work I hade to buy a small unit that held a spare key. The unit then would pick up the key signal and send it to the key-cylinder via a small wire, that I hade to wrap around the key cylinder, when the key-unit got power from the starter-unit.
So you problem could exist in your key, key cylinder, or worst case something in you computer. I don’t know a way of figuring out witch one it may be, but may be this will narrow you search.
I would start with a new key-cylinder….
