I have a certain amount of personal experience with air con systems due to my time as a jap importer, and only once, (and my own bloomin car!) have i known a totally goosed compressor, and that was leaking so appeared quite obviously as the fault.
exactly as FG suggests, if you put a (heavy Duty) power supply to the compressor positive and earth terminal, straight off the battery in substantial cable, see if the clutch on the end pulls in, and drops out instantly upon connection / disconnection.
this is bypassing the switches, sensors, and relays in the rest of the circuit, so is only testing the compressor clutch itself.
also as FG suggests, the regas.
you may not know to what level it was topped up, but if the chap managed to get it to kick in once, and never again, it sounds typically like the pressure is still low.
the compressor will only throw the clutch in with sufficient pressure and quantity of gas, and if it kicked in whilst being topped up, because you have to do it with the system running with a demand for cold air, then never again, it does sound like the compressor and clutch do work, but then the pressure/quanity level has dropped to below the neccessary to continue to do this once it had moved beyond the comporessor itself.
i know you state you have no leaks, and it has helf pressure over time, but do you know at what pressure?
finally, as i stated at the top, i have only ever known one totally goosed compressor, but, that was on my K reg 300zx, so it already many years older than yours will be, and coming from Japan, very likely had much harder use too, although having said that, most aircon issues tend to arise in this country because folk only think to use it 3 days a year for a blast of cold air on those balmy freak weather days we get.
aircon systems that are sat idle are begging for a breakdown, as the gas also contains lubricant and sealant to preserve the integrity of the systems internals, o'rings, pipework and the compressor itself, and quality gas also contains a visible flourescent to help identify even small external leaks. they should be used all year round.
even if you prove your compressor is Tatered, you can get rebuild kits, new clutch sections etc etc if you search the ole interweb long enough, and they will be precisely for your model and serial number unit, most likely from the states, but still very much cheaper than a new unit, even if you have to pay a local engineer to assist in doing it.
failing that, a replacement used compressor from someone such as Autolusso, or any other reputable breaker should be a good buy and come some sort of guarantee and test that it works, but i don't know what they'll charge for it.
finally, particular to the alfa's, the relays concerned in front of the battery often get tired, and their position often mean the connections get green and far from perfect. I'd swap a relay over for a known one and check that and the connections, and meter for the correct trigger signal from the actual control panel too, i.e. when you hit the air con button, the relay should recieve its trigger to throw over, this can be heard, felt, and measured with a voltmemter, so you can rule out any control panel faults pretty quickly.