windex is not always the answer.

what you would be better of doing, is getting more of your generic ink, and doing repeated cleanings. The ink has to pull the crap from the head there is no other option on the size and scale you (as a regular user) live.

If you were in a business that made and manufactured printers, you might have additional resources, including chemicals to flush through the head, but after the chemicals have gone through, you're still left with having to flush ink through there to remove any other chemicals' residue out.

The alternative, is to buy a new cartridge, your choice generic or HP .. and if that immediately works, then you know your old cartridge is finally at its deathbed, and is time to let it go. If replacing it with a generic doesn't yield significantly better output, then you have to question if its the head, or the electrical path of the printer, the contacts that touch the back face of the cartridge, etc.. and if for no other signs of problem you find nothing else to go on.. its possible the printer has died in a way that didn't cause it to alert you to that fact.