Remove the left cover of the machine and look on the backside of the ink supply station. I've got 2 360's and have had ink leaks in both recently that fried the ISS PCA boards. IMO, it's a design flaw to put uncovered sensitive electronics directly underneath the ink station, but it is what it is. The same issue can cause different errors, some continuable and some non-continuable, but the code you mentioned was one of the ones that I saw. The board can be damaged and in turn, it will mark the cartridges as "defective" and render them useless without a new chip.
If you remove the left cover and see ink where you don't think you should see ink, then it could be one of the PIP floaters and assembly is failing and needs to be replaced. This is very easy to do yourself. I've replaced both boards and a few of these PIP units on both of my machines. If you don't see ink anywhere it doesn't mean the board isn't still damaged, I've had that happen too. But do yourself a favor and put clear packinging tape on top of the 2 ISS boards to protect from potential leaks. HP can build a brilliant machine and then be a total dumbass about certain things.