Spent today tiring to bring back my AC system before a long road trip, was a no go. The compressor comes on but believe it is bad . So between shows will have to pull it to make sure I order the correct one for my brackets.
If the compressor comes on it should mean the system is reading some pressure in your lines. Though it may not be enough to actually cool. You can get a cheap gauge and can from an auto store and see if your system needs topped off.
Have & used an AC gauge set, compressor engages & have high & low pressure reading where there should be, both hoses are hot, so think pump is not pushing through the system. In 2014 I replaced all parts in the system except the pump, which I flushed & added the correct oil as change from R12 to 134A. and was working for a while. I don't use much at all.
I've read that using PAG oil during the conversion will kill the system. Maybe that could be the cause? Sounds like you've narrowed it down to the compressor already though.