If the compressor is kicking in, then there is gas in the system. You say it isn't cold enough, but compared to what?
My 156 has fully functional AC and just isn't very good!
My Ford Focus pretty much gets icicles on the air vents!
If it has deteriorated over time, either the refrigerant in the system has leaked out, or the system has got water in through the seals. This should be collected by the dryer, but after a while the dryer gets saturated, I've forms inside the pipes or compressor reducing efficiency.
The mobile units that many garages use are useless at finding faults. Try a dedicated AC specialist if you want it properly fixed, or a can of DIY AC refill gas of it just needs a top up. I have a nearly full can in the garage from an old Stilo which occasionally dumped all its refrigerant. No one could find where the fault was so every couple of months over the summer, a healthy squirt got it going again.