Greetings, sorry to hear you are having issues with your HP printer. I have had multiple HP injects and currently have a HP 8600 model. Unfortunately this is not an easy consumer fix. If you check out the this link on the HP support site the key http://support.hp.com/us-en/document/c04839288 you will note that the key statements on the page are:
This error indicates a hardware failure, and the printer requires service or replacement.
Your printer model might be replaced under the following conditions:
Bot***** *****ne, you can't fix it yourself and if it is out of warranty if is cheaper to go out an my a new one at Costco. At least this way you get a warranty again plus new ink cartridges. The high failure rate of ink jet printers is why my main work house printer is a many years old laser jet 3052. Since all of the critical parts get replaced with each new cartridge they last far longer, and print B/W cheaper and faster, that any inkjet.
Sorry I can't be of more help here, your unit need to be replaced by either warranty or the purchase of a new one unless there is some small repair shop with access to the required parts (check near your local college/university an dsee if any are near by) However, if the repair in more than 1/3 the cost of buying a new one don't repair it unless you just spent a lot of money on new cartridges that will not work on the latest printers.
Your printer is one of the models listed above.
The printer exhibits the error message: There is a problem with the printhead.