Having worked at an Epson and HP warranty shop for over 10 years, I can say many "compatible" cartridges cause significant issues. Blocked print heads is one. I have not worked for that shop for several years and have no interest in ink sales :-)
Epson cartridges normally have a very fine screen at the bottom of the cartridge above where it goes into the print head. This screen keeps dried ink particles from entering the print head. As the ink level goes down, ink dries on the sides of the cartridge and then movement allows it to drop into the tank. Many compatible cartridges do not have this screen. We cut many open to check this.
If the printer has not been turned off properly, it will also cause clogged print heads. It is important to turn off with the power button and allow the printer to properly cap the printhead/cartridge. Turning off with a power bar will assure issues like plugged heads/nozzles.
A good technician may be able to clean the printhead with a solution from Epson( or others) but it takes some time and patience. Given the cost of printers today, most will skip this due to cost.
There are some "kits" offered that have the cleaning solution and a syringe. One is here I also see some videos on the process online. The Epson fluid was red but I belive that was for easy visibility when cleaning. I would certainly check your local repair shops and see if they will give an estimate for a proper cleaning.
Also note there are absorbant pads under the print head rest position that can become saturated and must be replaced or you will have ink smeared across the paper.
As a side note, we tried two different compatible inks in an Epson printer and then printed the same image on the same high quality paper. The difference in quaility was clear to anyone who looked at the image. Epson ink was much better.
I called a printer company and they told me that the HP 652 Black and Color cartridges are NOT locked when the printer reads them as empty. They should still print normally.
The problem was that the cartridge was actually empty not filled.
Apparently I had very little ink in the bottle and when I pulled ink from the syringe it appeared as full because the syringe was sucking some drops of ink and appeared full at the walls.
I just refilled with full ink syringe and it worked just fine .... so the cartridge is OK and it does not need any kind of re-setting.
Best Answer
This has become a popular post so I'm copying over the answer from the official HP forums rather than linking to it.
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Hi,
Unfortunately it is not possible to print using the black and white while any of the ink cartridges are empty.
Using the Black ink only possible while there is color ink as well.
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HP forum post