Hi and welcome to Just Answer. My name is XXXXX XXXXX have been repairing Electronics Professionally for over 13+ years and currently own a Shop in FL.
This is more than likely a bad Print Head. I see this problem and have to replace them all the time but lets clean it's contacts first just to say that we tried everything.
Step one: Remove, clean, and reinstall the printhead
Step two: Reset the printer
If this doesn't fix the Black issue, the Print Head Pump for the Black has burned out and the Print Head will have to be replaced. This is a Foreign part and will have to be shipped internationally. You can purchase a new one from the UK for $60 here: http://www.ebay.com/itm/HP-OfficeJet-printer-printhead-1-colour-cyan-magenta-yellow-black-Marley-CN643A-/160738648035?pt=UK_CamerasPhoto_Printing_PrinterInkCatridges_JN&hash=item256cc51fe3.
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It's a foreign part. I've looked everywhere in the states and everyone's sold out. If you've dont the following and the black still isn't working then the Print Head is bad and will have to be replaced if you want to get the black working again.