I know nothing about computers, however, my printer was having a similar issue. Did you check to see if your computer and your printer are using the same wifi name and password? That was my issue because I had changed my wifi name and password on my computer but not on my printer.

I agree with @chyna that it might be your wifi, but a slightly different problem. An old printer won’t have 5G, and so you need to make sure your computer is using the non 5G connection. My wifi has two options, maybe yours does too. I find it easiest to test from my phone, because my phone already has both wifi set up. In fact, at the time I was still able to print from my phone, so I knew it was something with the computer connection to the printer and not the printer.

Also, my HP printer suddenly started having problems two years ago after never having a problem before, I really think HP infects their equipment to make it malfunction. Sometimes turning the printer off and on helps, and sometimes I could run the printer trouble shooter from my computer and it would fix it.

I would try the wifi fix that I mentioned first.

What’s the connection to your printer? Wifi, or USB cable, or ethernet? That will make a huge difference in diagnosing the problem.

Have you paired your printer to your WiFi??? I don’t know how to tell you how to do that, but I know it’s important to HP!!! I have Win11 with a HP 5000 series All-In-One. I held my breath through the setup because I found it to be confusing as hell!!! I had to FORGET everything that I knew about printer setup & just trust the HP directions!!! When I was finished, my 5000 series was setup, but I could NOT tell you how I did it because I don’t have a clue. My cell ALWAYS gives me a “not connected” error message. Still, IF I press OK, my print job goes through.

I don’t feel safe telling you to go out & buy an HP 5000 series printer because I feel it is a simple fix with the printer that you have…I just have NO clue what that simple fix is!!! I HATE the HP setup for WiFi…it is sooo freaking confusing!!!

One thing that I read indicated that this is a known problem with the 2600 series, so you might want to contact HP support to see IF they have an easy fix for you before buying another printer!!!

FYI…I did a search for ”I have an HP desk jet 2600 series and it won’t connect to it at all.” & all kind of things came up. Since I don’t know what all you’ve done up to now, you might want to do the same search & see IF you see anything that you haven’t tried.

Wish I could tell you since I keep having issues with my printer also staying connected to wifi. I also have an HP Printer only Officejet 5255. So frustrating. HP does not make their stuff user friendly.

If I were in your situation, I’d also consider going to my local library and have my documents printed there. My library doesn’t charge much (it’s much cheaper than a copy center), it’s easy, and the best part is there’s never a line.

This is quite common for Windows 11
Are you running wireless or cabled? Make sure it is on the same network. Many WIFI routers have a 5 G band that this printer will not connect to but your new computer will. While they theoretically should be on same network, in may not be set to bridge the printer communications.
Follow this HP site recommendation.
https://support.hp.com/us-en/document/ish_5866897-5876039-16

I have a HP printer that doesn’t like running on wireless, it dropped off all the time.
I run Ethernet now.

Perhaps the issue is that the printer goes to sleep so it doesn’t show up on the network. Press a button to wake it up, or turn it off and on again, then try printing again.