New printer scanner
 

Looks like our HP 6520, printer/scanner just croaked --looking for recommendations

Installed 4 new HP cartridges --still getting no black

HP printers typically have a software tool to 'clean' the print heads. Did you try that?

This may seem like a dumb question but are you sure you took all of the wrapping off of the cartridge? There is some plastic covering the ink hole on the cartridge that sometimes isn't so obvious.

Far from a technonerd but
 

I had an HP ink jet printer. If, you check your cost per page
in black and white it is posted at around thirteen cents and that I believe is in draft mode. I used to use mine regularly.
since we retired we used it far less than before. At less use,
it actually uses more ink. They use the ink priced similar to gold to clean the head. There are instructions on the internet explaining how to remove and clean the head.
Even the instructions say it rarely works. If, I recall the xl cartidges are like $27 each. So replacing the five is roughly $125. The head, assuming you need a new one is listed on line for ?????? about $75.

I do not really need to print color. I just bought a Samsung
lazar printer and scanner from Best buy M2070FW cost was
$149 new not refurbished. We've had it for about two months and it has been fine. Cost per print is listed at TWO CENTS a page. Typical of most of these items, they probably sell them at a loss, my HP was $99, but, they make a fortune on the INK. I expect I had put 700 to 1,000 in ink into a printer that I paid $99 for. Oh a big plus for me. The ink jet prints run if you get them wet. The lazar does not.

We've had have a Brother 2270DW black/white lazer printer for several years. It keeps on printing, even with the 3rd-party ink I buy. The downside is we have to have a regular scanner/copier too (Canon) to make copies of stuff. So far so good on the 3rd party ink I'm using in it.

A further suggestion
 

You report you put in FOUR new HP cartridges, If, that machine is the same as the one I had it takes FIVE cartrages.
CYAN, MAGENTA, YELLOW PHOTO BLACK AND BLACK. You say you are getting no black. If, I recall you could buy the cartridges individually or as a color kit which had only the four
colors.
Also, the contacts between the cartridges and the machine are rather poor-just a contact to a printed plastic tape. A flake of dust could easily prevent contact. I would try removing the ink cartridges one at a time and gently using compressed air or ear syringe or???? to blow it out.
I seem to recall on my HP if any cartridge is out it will not print. That does not match your post.
Unlike another post, that Samsung lazer black and white
M2070FW. I picked that one because it SCANS, as well as prints and as I said we paid only $149 for it. While mine is hardwired to my computer, it also can be used wireless and it will print from a smart phone. I think the one I bought is now discontinued perhaps why it was so inexpensive. If, I recall Best Buy was offering it at $179. While I was still trying to dfecide what to buy brands etc the price dropped and I placed my order..

Look up how to reset the printer. I had the same problem.

The 6520 was discontinued in 2015. It was known to have problems with the black ink not printing. It doesn't use photo black, just the 3 individual colors plus black.

If you liked the PhotoSmart series, you could go with one of the newer HP Envy Photo all-in-one printers. The lower-volume ones are under $100 and are HP Instant Ink compatible. If you print 50 pages per month or less, you could get an InstantInk plan that costs only $2.99/month, and the ink is delivered to you before you need it, and you don't have to order it. I have the HPEnvy 6255 with the 50PPM plan. My printer is noisy but the color output is fabulous, and having instant ink means I'm only paying $36 per YEAR for ink, since I'm low-volume. If you print between 51 pages and 100 pages per month, it'd be $4.99 per month. So that'd be around $60 per year. You don't get the cartridges monthly. You get it based on when your printer is starting to run low on ink. It's all done wirelessly so your printer would need to be hooked up to the internet, or to your internet computer.

Staples has the 7155 on sale at $89.99.