Hi, thank you for contacting JustAnswer.com. My name is Russell. I will do my best to provide the right answer to your question.
I think you should try a certain cleaning procedure that I have found effective, first.
1. Clean the (cyan) printhead.
2. Wait 1/2 hour to several hours or overnight, leaving the printer On but unused (no print jobs, etc.)
This allows waste ink to soak into the printhead and hopefully dissolve dried ink etc.
3. Clean the printhead a second time.
4. Wait again (as in step 2 above) for 1/2 hr. to several hrs., printer On but unused.
5. Clean the printhead a third time.
Then test whether cyan ink is showing up at all in prints at this point. If it is, even faintly, then repeating this procedure will (eventually, at the cost of a certain amount of ink wasted in the process) clear up the clogged printhead.
After that fails, if it does fail, what you need to do is to decide whether replacing the printhead (which will cost something considerable, more than you would think usually) is better, given the printer's age, or whether it would be more preferable for you to replace the printer altogether with a new one (and hopefully recycle the old printer, always a good idea.)
So try the triple-cleaning-with-wait-times that I recommended, and get back to me if it doesn't work for you (so I can advise you further...)... or if it does help (- I always like to hear that something I recommended has worked!)
NOTE: If you decide to dispose of the printer, rather than have it serviced, nor try the printhead replacement (it is a rather old printer after all), then there is a good option for disposing of your HP printer! Let me know if you reach that stage and that decision, and I will inform you how to make use of your best options for HP printer disposal.
Let me know how it goes, please. Thanks.