Air compressor Saturn astra

I would check the compressor to make sure the clutch is kicking in. If that seems to be working then I would just put some Freon in it to see if that would fix the problem. Hopefully that will fix it if it doesn't it's something more serious .

The anti theft protection is working put the security code into the unit and it should work

If you know for a fact the system is charged, you'll need a wiring diagram to track the circuit from the switch and relay to the clutch. Could be one of several components.

Air compressor or A/C compressor (Air conditioner)?

either you have a very bad battery, or your not guetting fuel for it to start.

see this steps and think with clearly and logically NOT feared. God bless you
Start with the compressor. Does it engage when you turn on the A/C?
If so, the compressor is working and the A/C system probably contains enough refrigerant to make cold air, so the problem is inside the HVAC unit. Replace the motor that controls the blend air door (this is a difficult job and best left to a professional since it involves tearing apart the HVAC unit -- about an 8 to 10 hour job!).
If the compressor does not engage when you turn on the A/C, see if it will run by jumping the compressor clutch wire directly to the battery (use a fused jumper wire). If the compressor works when you jump it, and the A/C blows cold air, the system contains refrigerant and the fault is likely a bad A/C compressor clutch relay or a bad clutch cycling switch or pressure switch.
If the compressor does not engage when you jump it, the problem is a bad compressor clutch.
If the clutch engages but the compressor does not turn (the belt will start to slip and squeal), the compressor is locked up and you need a new compressor.
If the compressor clutch engages and turns the compressor, but the A/C still does not blow cold air, the system is probably low on refrigerant and needs to be recharged.

The main reason this happens is because all the doors are not unlocked.

The fuel door does not have a release button, it relies on the door unlock button.

Press the door unlock button in the middle of the dash. (the button with a key on it)

This should release the fuel door and you can fill it up

Need confirmation that the AC adaptor for Duralast jump start model BP-DLG is a 12volt 450ma. Is this correct or do I need something else?

You should be able to try it immediately, or whenever you need to.