Good Day. Thank you for posting your query in the HP community. I read the post regarding assistance with ink cartridge errors. I will be delighted to assist you here.
Superb description and spectacular troubleshooting and commendable diagnosis of the issue before posting. Kudos to you for that. 
For better clarity and to assist you better I would require more information regarding this:
- Did this happen after a power outage or surge?
- Did you replace ink cartridges and check again?
For now, try these steps:
- Perform a hard reset on the printer from this link: https://hp.care/2kcz5os (Step 1: Reset the printer)
Then from this link: https://hp.care/2pP26Xt (HP OfficeJet 3830, DeskJet 3830, 5730 Printers - 'Cartridge Problem' or 'Cartridges Missing' Error) perform all the prescribed troubehooting steps.
- Step 1: Make sure that the ink cartridges are compatible
- Step 2: Remove, inspect, and then reseat the ink cartridges
- Step 3: Clean the ink cartridge contacts
- Step 4: Remove and then reinsert the ink cartridges again
- Step 5: Clean the ink cartridge contacts again
- Step 6: Restart the printer
- Step 7: Replace the ink cartridge
- Step 8: Align the ink cartridges
- Step 9: Service the printer
Now check if the issue gets fixed. If it persists, then replace the problematic ink cartridge either by contacting HP phone support or by contacting a local store like Best Buy or Staples. This should fix the issue as long as the printer is not faulty. if the printer is faulty, then THe printer needs to be replaced.
I am being honest about it by keeping your best interest in mind without beating around the bush.
HP Technical Support can be reached by clicking on the following link: https://hp.care/2moMFSc
- Once the support page opens please select the country in which you're located. Next, enter your HP model number on the right.
- Next, choose the 'Contact Support' tab at the top and scroll down to the bottom of the 'HP Support- Contact' page to fill out the form provided with your contact information.
- Once completed click the 'Show Options' icon on the bottom right.
- Lastly, scroll down to the bottom of the page and select 'Get phone number.' A case number and phone number will now populate for you.
They will be happy to assist you immediately.
If the unit is under warranty, the manufacturer’s warranty should take care of it for you.
Good luck and keep me posted. I wish you well. I will keep a watch for your response.
Please perform all these steps patiently as it is critical to resolving the issue. Going by your technical expertise and competence I am sure you will be able to perform these steps without breaking a sweat.
Hope this helps. Let me know how it goes. To simply say thanks, please click the "Thumbs Up"button to give me a Kudos to appreciate my efforts to help. If this helps, please mark this as “Accepted Solution”as it will help several others with the same issue to get it resolved without hassles.
Take care and have a blessed week ahead.
Cheers!