black ink doesn't work

Depending on the age of your printer, with all inkjets, they regularly use ink to 'service' itself. Where does this ink go then? In a reservoir in your printer. This is why they tell you not to tilt a printer, because there is typically a pool that this ink will fill over time. If cleaning the printhead did not work, I would suggest partially dissasembling the printer to remove the pads that are also used to absorb this ink and running them under a stream of warm water until ink stops coming out. After waiting for them to thoroughly dry, put it back in and start it up. These pad are located on whichever side the printhead parks and can typically be fairly easily removed once you get the outer casing off. As I mentioned, there is a resevoir where a pool of ink would be, and would empty that as well. If you have ever tilted your printer, then you may find huge gobs of ink in there.