There are different fittings for different types of refrigerant. Unless something highly unusual was done, which would be illegal, so a professional shop would NOT have done it, if the fitting connects you have the right refrigerant.
This AC System has NEVER been opened, lines disconnected, suffered a sudden massive leak, etc, CORRECT? If air or moisture has gotten into the system, then the entire system needs to be flushed, the filter/drier replaced and a vacuum drawn for 30 minutes. Any air or moisture in an AC system will form acids that will eat right thru it and destroy the AC system.
You need to understand how the AC system works, there was nothing wrong with what you were seeing, you just didn't understand what was happening.
http://home.howstuffworks.com/ac.htm
How much is this AC System worth to you? I ask, because it is VERY EASY to destroy an AC System if you don't know what your doing.
If you really aren't that concerned with the AC, its worth the $10 for a can or two of refrigerant to get it working for a while, if you can. Then Proceed on your own, you do risk destroying the AC System.
If you really want a proper working AC System. Then take it too a professional and have them repair and service it properly, OR do the research, learn how to service it and spend the money on the tools you'll need to do it at least Half-Properly. Otherwise, you risk destroying the AC system and it will take 10 times as much money and effort to repair it.
Believe me, when it comes to AC, when most people think they are doing a "Half-A$$ Servicing" are fooling themselves and they are really doing a "Full-A$$ Servicing".
Having said that, a likely scenario is that the AC system has a slow leak and leaked enough refrigerant over the years that the low-pressure cut off is preventing the compressor from turning on.
If your LUCKY, you can service with close to the right amount of refrigerant and oil (you'll have to guess) and it will work alright for another year or two before needing more refrigerant. BTW, its illegal to service an AC System with a known leak, unless you at least attempt to repair the leak; yea, I know, who's going to catch you.
In this case, you have to add refrigerant to the low side fitting until there is enough pressure in the system to throw the low pressure switch to allow the compressor to engage. Once the compressor engages, it will pump what refrigerant you have in there thru the system, which will cause a pressure increase on the "Hi-Side" of the system, and a pressure drop on the "Low-Side" of the system. Since you barely had enough refrigerant in the system to just build enough pressure to trip the low pressure switch, once the compressor engages and drops that little pressure you had, the low pressure switch trips back again and shuts down the compressor. Its called a Cycling Compressor, a Common Symptom of Low Refrigerant Level. It will continue to do that, until you add enough refrigerant that the compressor can pump it thru the system without dropping pressure on the low side enough to trip the low pressure switch. There is a sticker under the hood that should tell you how much refrigerant the system holds, buy enough cans to add that much minus 2-3 oz, that hopefully was still left in the system. You should add 2 oz or oil or more (look around the AC system, if you see signs of leaking oil, add more) since a leaking AC system will often leak a little oil with the refrigerant. If its a R-134a system, it should be PAG Oil, do some research as too what weight oil for your system. Too much Oil can decrease performance a bit, but too little Oil will damage the compressor. Continue servicing with the refrigerant can, switching once they are empty (it take a long time for each can to finally boil out the last of its refrigerant, dropping the can into a bucket of hot water while its connected can speed it up). Stop when you've added the amount of refrigerant you figured out that it needed. You may have already messed that up, since you only added part of a can, probably losing some in between. Another technique, watch the low side return from the evaporator, hopefully you live in an area humid enough to do this, once that line starts to collect a significant amount of condensation, NOT just foggy layer, a full sweating beads of condensation, and the compressor stays on without cycling, you should have close to the proper amount of refrigerant.
This is all ASSUMING that you just have a minor slow leak and there was still enough refrigerant left in the system to maintain an OVERPRESSURE with ambient pressures and keep any air/moisture out of the system, that the system has NEVER BEEN OPENED. A fairly common scenario, but hardly the only scenario, with many many different problems that are possible in your AC system, so you run a big risk of destroying that AC system.