car will not start or key will not come out and will not shift out of park

You can change the BCM but your mileage will not be correct it will have to be programmed and pass lock sensor will have to be learned as well.

2007 Saturn Outlook will not start or key will not come out and will not shift out of park. What should I start with to identify the problem? The lights come on and it turns but the vehicle won't start.

This sounds like a shift interlock or even a transmission range sensor issue. The fact that it won't start points to the range sensor but the other issues are more indicative of a shift interlock. The range sensor tells the engine computer what position the shifter is in so that it knows it is okay to start the vehicle because it is in park or neutral. The interlock holds the key from releasing when the vehicle is not in park.

I would suggest starting with monitoring the PCM data with scan tool to see what it says for the current gear. It should say park or neutral. If it says drive, reverse, or is blank then the range sensor is your issue. Clearly we are going to need a scan tool capable of doing this so our options may be limited if we don't have one.

At the very least, I included the process for the solenoid that you can try and access and see if the contact is not operating. If you manually press the contact down it could release your key. Then you know that part of it is the interlock issue. As for not starting we can tackle that separate. However, my guess at this point is they are related.

Let me know and we can go from there.