I normally substitute a test lamp across the compressor connector with the A/C on.
If the lamp is it, the compressor clutch is open circuit.
This happens on a majority of cases.
The ECM is generally the next cause for no A/C.
Are you quite sure it has the right weight of gas?
It will not work if that is the case.
Yes, the black box you see under the front is the cooling module.
Because yours has this module, there could be a problem here that is the cause of BOTH of your problems.
Not all Astras have a cooling module.
Now you need a TECH2 diagnosis from a Holden dealer to see what the cooling module is doing.
Has the car had any impact damage in the LHF?