Have you tried starting then quickkly whip a plug out and see if it smells of fuel?
I know you have no spark, but on the EFi system the two could be linked....
The ECU gets an engine running signal from the coil firing, if it doesnt get that it won' t add fuel,....if the plug smells of fuel, then the system thinks the coil is firing and as such engine is runnng.....if there is not smell of fuel, then the ignition circuit LT needs looking at....
Have you checked the ignition amp as these are a common cause of issue.