Problem with HP DesignJet. The cartridges are functional and the contacts are clean.

[Mikl153]

The cartridges are functional and the contacts are clean, but it says the cartridges are faulty.

[BeemerBiker]

Possibly the PC either has or simply gets old information from the printer when you check the ink levels.

1. Unplug printer from the wall outlet.
2. If the power cord has a transformer (wall wart) unplug from the printer also.
3. Press the power button 2-3 times to discharge residual electricity.
4. Wait 60 second then plug into wall (not UPS nor surge protector) and turn on.
5. Reboot your PC.

Another possibility is the electrical contacts on the cartridge (or the printhead) have ink debris, or tape / glue residue.  You may have tried this already but please look through the below procedures.
Expand the Spoiler for cleaning advice

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General advice on printhead cleaning is here.
This link shows cleaning the 8600 printhead and removal is shown here. This video for 86xx is good
This is another type of printhead cleaning, different from the above.
If it has been 2-3 monthes since last used, possibly soaking the cartridge in hot water will reflow the ink.

Cleaning and removing ink is shown below by our "Scullery" team.

An HP original video on how to clean the printheads by our experts. Yes, this can get messy, but it works. If your ink levels are good but you are printing blank pages then this is likely the solution.

Official HP advice on cleaning.

Some printers have a printhead cleaning procedure.

To clean the printhead on an HP printer, access the printer settings through the HP App, navigate to "Print Quality Tools," and select "Clean Printhead"; this will initiate a cleaning cycle where the printer will automatically run a cleaning process to clear any clogs in the printhead

Inkjet and printhead cleaning kits are available

Consumer inkjet printer printheads typically last for several years, with some lasting up to 10 years or even longer. However, the lifespan can vary greatly depending on usage, maintenance, and environmental factors.

How many total impressions (pages) have you done?

If you have a tank type printer there could be air in the lines.
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To prevent bubbles from forming in the ink tubes, keep the ink levels above the minimum line, refill the tanks before they run too low, make sure the tank caps are closed securely, and avoid tilting or transporting the printer unnecessarily.

If you have bubbles

HP's SupportGPT recommends using HP Smart (or the HP App) to run HP's clean printhead function that many of our inkjet or tank printers have.

Google's AI provides a fallback in the event the maintenance cycle fails

• Turn off the printer: Power off the machine and safely open the access doors to expose the ink tanks and printhead carriage.
• Locate the air bubble: Visually identify where the air bubble is trapped in the translucent ink pipe.
• Manually push the air: You can often gently tap along the ink tubes to help the air bubble travel up into the main ink tank reservoir.
• Use a syringe (for stubborn clogs): If tapping fails, you can use an ink refilling syringe (often found in printer cleaning kits). Remove the ink cartridge or damper inside the printhead, attach the syringe to the ink outlet, and gently pull back on the plunger until ink flows smoothly and the air is drawn out.

OpenAI states what not to do

Don't squeeze the ink bottles while they're installed.
Don't try to force ink through the tubes with compressed air.
Don't use a syringe on the ink tanks unless you are experienced with HP ink systems—it's easy to damage the pressure regulation or introduce more air.

Let me know what you find out.