just when you turn it to start you hear a click noise
With regards to the park/neutral switch, ignition switch and such let me reiterate,,, if the starter relay (#47) in the fuse box clicks every time you turn the key to the start position this in itself proves that the park/neutral switch and the ignition switch are working correctly at least as far the starter is concerned. You can see this in the wiring diagram. The signal telling the PCM to engage the starter relay comes to the PCM through the crank fuse from the ignition switch. This tells the PCM that you wish to start. The PCM checks for a signal from the Park/Neutral switch. This signal can also be seen in the same wiring diagram where 12volt power comes through the ign E fuse down to the Park/Neutral switch then back through the fuseblock and on to the PCM. If the PCM does not see both of these it will not command the starter relay to engage and you will not hear the click in the fusebox.
If I were troubleshooting it at the stage where the starter relay in the fusebox clicks but the starter does not engage I would do the jumper as directed in the video I linked in my last post. The video author cautions and I will concur, do not stick test light probes or other such items down into the fuseblock. They are too thick and will likely do damage to the connectors down in the hole. The relay terminal pins are just 0.7 mm thick, even a standard small paper clip is thicker than this. If larger things are stuck down there they will likely spread the connector apart then the relay will have poor or no connection to the fuseblock resulting in intermittent no crank conditions. This I know firsthand as my TrailBlazer was in this condition when I bought it.
Now as for the security stuff,,,I have no idea what is done to a PCM to remove the VATS stuff so I can only speak of a standard system ....I may be wrong but I think the PCM will not command the starter relay on before getting an OK from the BCM saying essentially that the ignition switch has been turned using a good key. So again, if the starter relay is clicking then this appears to be OK. HOWEVER,,,,, the security can still cutoff the fuel supply AFTER the engine starts if other security related things don't check out right. But you're not there yet. You are not even cranking so that should be the first priority.
Battery issues. You said the battery loses charge as soon as disconnected from the jumper vehicle. If your battery is poor or dead this is normal behaviour. Your battery will not charge up when hooked to a jumper car unless it is hooked up to a running car with a good electrical system for at least an hour or more. And this is not anything I could recommend as it is bad for the donor cars charging system. The purpose of jumping is only to get the dead car started. A discharged battery needs to be charged on a battery charger for at least an hour or more. So if your battery is in poor charge that needs to be addressed. Even with a good donor to jump from, if the jumper cables are not heavy enough and the connections are not quite solid enough at the batteries you can get a big enough voltage drop (loss) to cause the sort of things you are seeing. You hook it all up, turn the key to start, the system does all it is supposed to and when the big load of the starter tries to engage it draws too much current through the bad connections of the jumper cables or the cables just are too small and the voltage drops down to where there is not enough power at the dead car and the system resets and the whole thing repeats. This is what causes that click,click,click,click you sometimes hear when trying to jump start a vehicle.