In some of our earlier conversations I didn't trigger on the fact that disconnecting the battery will cause the short to ground to go away. Likewise, the switching the key off to on rapidly doesn't always result in a ground condition. This means the driver transistor in the PCM isn't shorted, but still able to turn on and off normally. Maybe you should try unplugging the camshaft position sensor to make sure it isn't somehow stuck and telling the PCM to fire the injector. I'm not sure what other sensors would come in to play for base injector firing.
-Rod