New ink installed, will not print --?

*Read: I know this because I often pick these up for nothing and use them as a cheap scanner.*

With Epson, it’s almost always a hardware flaw—a clogged printhead. Epson integrates the head such that end user removal is not viable. If I have nothing to lose, I'll probably get it done, but I know how. At this point, the clogging issue is a known and established design flaw that needs to be addressed with special cleaners when it happens. It can be fixed by cleaning the heads more often, but Epson refuses to do so to make their ink yields not look like a lie.

This issue is usually caused by OEM Epson ink (and is compounded with false “security updates”, which block 3rd party ink carts). The pigment inks are far worse than the dye inks when they clog as the pigment ink is heavier and harder to clear out; but both are affected. In other cases it's caused by air in the printhead, which is usually more in line with inconsistent print quality rather then a hard nozzle failure.
The air issue can be fixed by forcing the air out of the printhead. If it’s clogged, cleaner can be found on eBay. NEVER UPDATE THE FIRMWARE ON EPSON PRINTERS! Let them live with the fact their BS “security updates” leave printers open to attack.

PS: I used to love the Epson printers for scanner use, but after the black cart bait-and-switch firmware, I’m pretty much done with anything Epson—even used. They have some of the best scanners I’ve used, but the firmware issue makes it hard to know if it will be cheap or expensive to put ink, especially if I don’t remember the WIC usage and waste ink pad saturation.

However, as much as I want to tear into Epson, they’re no worse than HP with the dynamic security printers, which is a way to block 3rd party ink over time progressively. The difference with HP is that they DO allow you to use the printer with the original chip, while Epson disables it - HP only cares about the warranty for the most part. Eventually, the clone chips bypass the dynamic security (and HP is no longer maintaining new firmware releases, ~5 years before this happens). It's still best to avoid updating the firmware if you can avoid it. At least HP is honest, unlike Epson. HP also has cartridge protection, which “locks” the chip to that printer, so you usually need to kill that before installing the ink if possible, or you can burn the first set and turn it off.

Lexmark was also guilty with the 100 series printers. They used RFID chips and forced you to replace the ink with those printers once it ran out, especially with the single-use return cartridges. You could replace the chip and use them again, but Lexmark is/was very sue-happy if you try and reuse a “return program” cartridge. They also made it quite a pain to do, but they have since walked from the inkjet market and made the lasers with the quality and moderate DRM HP used to make. Ironically, I'm happier with the modern Lexmarks more than modern HP now—same return program games, but what a 180.

These inkjet printers clog from non-use by their nature, but Epson is the worst of them all for it. You can fix it on most Canon models as long as the head is modular (not on all models), so they get a (partial) pass. It’s usually the low, low-end CLI models with fixed heads. However, they kept it modular on the higher-end ones.

On the more current 564/901 HP models, HP generally integrates the head and needs setup carts to use the printer again—and you probably no longer have them, so you can no longer use it once you lose the initial calibration. To get a properly serviceable inkjet nowadays, you need a wide-body HP 95X/96X printer (OfficeJet Pro) for a user-serviceable printhead with HP today if you have to give them your money. Canon is the current "tolerable" inkjet of choice today.

press the ink cartridge s until they click into place

When taking it out of the box there is a plastic sticker over the hole where the ink comes out make sure to remove that. Try taking your ink out and put in back in. Try resetting your printer.

My Xp-410 just stopped printing any visible marks whatsoever on the paper.

I confirmed printheads functional but no ink on paper. Did a reset except for the network settings and printer regained functionality. Bizarre!

I took it out again shake the cartridge and put it back on and start.

I had similar problems with adding new ink cartridges not working but as someone suggested previously, ( and it’s not mentioned in the instructions) if you pull off the small round clear plastic on each nozzle, it allows the ink to get in !

Worked for me :)