it's an HP officejet 4620. I know, it's old.... but it was working great and then...
I always use HP brand carts
I replaced the red because it ran out. All was well. Couple days later, black and yellow just stop printing. Both were low, but still operational. Until that moment. I've cleaned the printer heads a bajillion times with using the system. I've looked it up and did the flush with alcohol thing to clean them manually. I've gotten the yellow almost good again. I replaced the black cart because it did seem like that may be gone but there is nothing coming out of that.. It acknowledges cart is genuine and full. It makes like it's printing but the page comes out blank. I need black more than anything. please help

This happened one before and beest researched and fixed it and I think i did all the same things but evidently not.
I just can't be dealing with buying a new printer now, financially or emotionally. Please just trust me on the latter rather than debate it.
Can anyone help?
thank you