First make certain you have the interior (heating) fan set to high, if it is off then the system will not run and the LED behind the A/C button flashes.
Second I believe that if you turn on the A/C and run the engine the engine fans will kick in in order to blow air across the condenser (radiator) for the system. If they are not working it might cause some kind of trip as well.
I believe that the A/C needs the engine running as the pump runs off the engine that cools the gas so this would be normal. Also when you switch the engine off my Aero defaults to no A/C on next start all the time so you would need to switch it on again. I could be wrong, I have not been out in it for a bit.
I had a similar issue with my S2.
It ran out of gas, the compressor (pump) then dried out and failed due to the lack of gas which also acts as a lubricant I am told. It would turn on and give a very weak cool draft but nothing useful.
Get it pressure tested then depending on the results get it re-filled with fresh gas. At this point you may still have a dead pump.
In the end I had compressor, condenser (radiator) and some pipes replaced. Not cheap. The compressor is especially difficult to find.