I got a second hand a/c unit from someone recently. It works. It turns on, it blows cold air. But It doesn't blow cold enough air, and doesn't seem to keep working until the room is actually cool. I tried it for 3 days to make sure it just didn't need time to cool down the room. It is one room. My thoughts so far are that it isn't getting cold enough, or that the condenser just isn't running long enough. Cold air coming out doesn't always mean it's as cold as it should be. Sometimes, seems like it blows more hot air than cold. Kind of defeating the point of having it. Is there a single part, or something I could do to check or fix this? I don't want to have to buy yet another a/c. I just want to be able to fix it.

I'd also like to add that there is no water going into the water drain, or even really being produced. I checked for clogs, and there were none.