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.
Before throwing it out the window, it's worth taking a pencil eraser and rubbing off the ink head contacts.
Ambient humidity whether you live near the ocean or if your particular printer was mildly defective... can tarnish copper contacts.
A pencil eraser rubbed as gently as you'd erase a word off paper can rejuvenate electronic devices from cell phone batteries to your printer.
I can't hurt and you'll be surprised how effective it can be.
In every HP I own, I can still find ink in places you wouldn't think, take a dry (non Puff's moistened) kleenex, paper towel or toilet paper and rub the printers cartridge tray for any ink and this will be your culprit.
If you have ink accumulation, using high concentrate rubbing alchol dabbed paper towel to dlean it then immediately dry it will rejuvenate the printer
These are worth trying before kicking it out your window, but kicking an HP printer can be immensely satisfying .
Best Answer
The Officejet 8710 is among the HP printers that cannot print if any ink cartridge is empty (there is no override provision as some printers have). If any color cartridges are low, you can set it on black-only to minimize the use of color, but the color cartridges cannot register as empty.
Per the HP Customer Support Knowledge base (excerpts):
There is more explanation at that link.
Additional Discussion
HP's position on the printer not operating with an empty cartridge is based on a premise that the printer could be damaged otherwise. So there is no way around that without hacking the printer (which would void any warranty, would be very difficult to do since the firmware is proprietary, and stands a good chance of totally ruining the printer). The printers are inexpensive, and nobody stands to profit from investing in figuring out how to do it. So I wouldn't expect to see any kind of workaround for this.
However, there is potentially a way to get it printing again at less cost than buying HP ink cartridges. The OJ 8710 is among the HP printers that employ a security chip. This locks out the printer if it detects a "counterfeit" ink cartridge (which is for your benefit to ensure that you get the very best printing experience from your HP printer). :-)
For some printer models that didn't originally come with this "feature", HP implemented it surreptitiously through a software upgrade. There was heavy pushback, threats of legal action, etc., and HP decided to rethink its policy. They now have an optional software upgrade that can be manually downloaded from HP if you know about it, which will turn off this verification and allow the use of non-HP or refilled HP cartridges.
Just a warning, some other printers have an option to turn off the check for OEM ink cartridges. When you do it, it disables a lot of advanced features in the printer driver software, and they claim that if the printer malfunctions, you're on your own. So they let you do it but strongly discourage it. I don't know if that applies to your model, but you might want to inquire.
This info page from HP describes the use of the "security feature" and states:
This seems to be saying that the feature only addresses third party cartridges manufactured from scratch, with a non-HP chip. That would still leave the issue of original or refilled cartridges that claim to be empty based on character count, and prevent printing even though there's still ink left in the cartridge. But at least you could buy a new, unneeded fake cartridge for less than the cost of a new, unneeded HP cartridge. Ah, the joys of inkjet printers.
But here's a link to the HP Customer Support Knowledge Base that describes turning this off for your printer. However, your model is included in a group where manufacturing date appears to determine whether you can disable it:
My reading of the information is that for printers manufactured earlier, the provision wasn't clearly stated, so HP is letting people disable it. However, ones manufactured later clearly stated the policy on the box or in the user manual, so buyers were forewarned and out of luck.
I found online discussions saying that HP re-reconsidered, and other articles saying no, not really. So it looks like if the printer was manufactured before December 1 2016, you can probably disable the security chip feature and use less expensive third party cartridges. If it was manufactured later, maybe it can and maybe it can't. The situation is clear as mud. But that link will at least get you to the right place to find out; maybe just try it.