BCM allows instrument cluster lights to come on.

The Body Computer doesn't control the Engine Computer. First tap on the automatic shutdown (ASD) relay to see if the contacts have arced together and are sticking. If that doesn't help, pull that relay out and measure the voltages on the four outer terminals. At least one must have 12 volts all the time. On older models the wire coming from the ignition switch got 12 volts when the switch was turned on. Newer models are different. I'll have to search for a service manual to see how yours is wired. If you find 12 volts on a second terminal, start to put the relay back in and feel if it clicks when you do.