Failed AC is one of the biggest PITA to fix but don’t let it phase you, it’s not actually that complicated.
If you were to remove all the parts and lay them on the floor there is not that much too it.
You have to, as above advice, go through it with a methodical mind.
Assuming the HVAC unit is not at fault.
Number one would be to have the system vac check, gassed and oiled. Check again a week or two later and note the charge and discharge amounts to prove the system is holding.
Next, you need a compressor that is engaging (ping) and compressing.
Two ways to check this, 1. Listen for the clutch pinging and engaging or visually watch for the front pulley to engage and disengage. 2. Check the pipes are hot, cold or chilled. If the cabin fan is not working or stuck on one speed (thermoresistor) the AC will not engage the pump/work properly.
Pressure switch is where I would look next, you can pull the plug off it/bridge it to see if it makes any difference.
Finally, I would replace the condenser and dryer filter. Working but in efficient systems usually come down to a blocked dryer filter sometimes caused by too much oil being added to the system. Oil should be 15-20ml max, too much and the system clogs and you won’t clear it. We pulled 360ml from a system recently which was acting like yours. New condenser and dryer required.
A correctly working but inefficient cooling system should still cut the fan in and out. If it’s not, you need to determine that first.
