Backfire-after turning key off
Nope. The ballast is bypassed when cranking, so if ballast is bad it will try to start, but die in run.
My guess is a short on the coil -, or bad transistor in ECM. When you turn it off, you get a spark, but it is not in time with engine.
The other possibility is pickup related, faulty, gap too wide, or connector issue.