There are a few possible fixes for this. I'm not going to list all the instructions here,

but here a few things to try, assuming you've already tried the general reset

procedure mentioned above:

Here is one of HP's official fix procedures for this problem:

HP OfficeJet Printers - Resolving 'Problem with Ink System' Error

Below, is a list of some of HP's suggestions from the above link, as well as some procedures which are definitely NOT HP-AUTHORIZED. Some steps involve (minor) risk of damaging the printer if you're not careful, or don't follow instruction carefully.

1. Make sure you're using cartridges that have not dried up/clogged, and that still contain wet ink. I shake them to listen for the liquid inside.

2. Clean the gold electrical contacts on the ink cartridges, and clean the contacts on the printhead, that connect with the ink cartridge . (as per webpage linked above).

3. Inspect the carriage path for obstacles (as per webpage linked above).

4. Clean the printhead/nozzle. If you want to do this the way HP recommends, read the instructions linked above, or watch HP's own video detailing the process.

HP's video tells you to do this with warm, distilled water, which is gentle so presents lower risk, but water doesn't always unclog the inket nozzles to fix the problem.

Others perform this step with commercial inkjet cleaner formula. Some people use their own formula made of alcohol and original Windex. Best viewed on Youtube. Cleaning with anything other than water is NOT according to HP's instructions.

5. Remove the ink cartridges, then remove the printhead. Reinstall the printhead, and reinstall the ink cartridges. Note that HP's documentation states you sometimes have to do this 3 or even 4 times for it to take effect. You can see this in HP's documentation on their website about resolving this error. As shown on HP's webapge, and also a video hosted by HP.com . There are also videos on Youtube which show this.

6. Check the CMOS battery. Apparently a dead CMOS battery can cause this problem. I'd only recommend this for people who aren't too scared of taking things apart. It's pretty tight in the side of the printer where the logic (circuit) board sits. That being said, if you have steady hands, are patient, and can follow instructions, well, give it a try.

HP Officejet Pro 8600 CMOS battery location and replacement

7. Some videos tell you to do what HP calls a Semi-full reset to fix this problem. A semi-full reset is a sequence of keys on the control panel that you press that resets certain information in the printer to original settings. This sometimes makes the printer "forget" cartridges dried up, ink was not recently pumped, etc.

See this video for more info:

How to Fix the HP Ink System Failure!

However, I have scoured the Web and can't find any way to initiate a semi-full reset if you are stuck at the "ink system failure" error. If you are not stuck at that error, then a semi-full reset is well worthy trying.

8. Some documentation suggest doing a firmware update on this printer may clear this error. As with above, I haven't found way to do that unless you're NOT stuck at the error message in question

9. Make sure the printer is plugged directly into a wall outlet, and not into a UPS, power bar, surge protector or similar. Supposedly, that can cause the problem as well.

10. Check the inside of the printer for spilled ink. This can jam things up or trigger sensors which are not what you want. I'm not sure what chemical to use to clean spills, but that would most likely be in the Youtube videos.

11. Try using aluminum foil or wire to bridge contact that may lose continuity on the inside of the printhead circuit board. See this video for details:

How to fix inksystem failure for HP 8600, 8610, 8620, 8630 Print Heads

12. If all this fails, your last option is that the printhead is likely damaged/worn out. New ones are expensive. You can get them from HP, but they are cheaper (esp. used ones) on eBay.

Would love to view a service manual for that printer.

:-)