You can buy a injector test bulb to plug into the injector plug at almost any auto shop. That should sort that. Im not real handy with the v6's. But like any car, you need to make sure you have fuel pressure, spark and injector pulse.
If ur missing one you need to make a list of the causes, and eliminte them. It will be somewhat difficult to eliminate some of the issues you have because your running without a BCM. speed sensor will not stop it starting. Missing injector pulse is usually a symptom of the imobiliser, but can b other things.
One thing you could focus on is getting the engine light setup, so you can begin to pull error codes from the ecu, this will aid you greatly in getting to the bottom of it.