Okay. One can of refrigerant will not put enough pressure in the system to allow the compressor to kick in. The low pressure switch shuts off the compressor to protect it from low refrigerant level. Without adequate refrigerant, lubricant does not circulate, thus will destroy the compressor.
So now you have contaminated the system with whatever "alternate" refrigerant you added to the system. There are all sorts of problems involved when introducing incompatible refrigerants and oils. If the oil is incompatible it will not circulate thus destroying the compressor. If the refrigerant mixes with another refrigerant or moisture acids will be created that will eventually eat a hole in the evaporator or other components.
Had you not contaminated the system, you would have been able to simply find your leak, repair it and recharge with R12. Now that the system is contaminated, you will have to break all connections, THOROUGHLY flush the system, remove the compressor and pour out the mineral oil, then put in the correct amount of oil, replace the filter drier, evacuate and recharge.
This will be necessary regardless of the refrigerant you choose. You only have to go through this process if you want to have a system that will live for a long time. There are other things that people do all the time to get a/c, but most of them are short term solutions.
It's amazing how $30 per pound refrigerant cost causes people to do all sorts of things that cost them hundreds or thousands of dollars. Penny wise and pound foolish.
Since you are at this point now, if you are lucky the pressure that is in the system will force some of the UV dye out where you can see it. Start at the easy to see connections and around the compressor shaft seal.