Newer ink carts have a IC chip buried in them or the printer acknowledges such chip and if it sees it's too old date, it won't accept or causes issues. There are IC resetters setups that suppose to counter this but that is something for non-OEM ink carts or refills. While you state its a new ink cart from non-OEM source, it in itself could be past dated, doesn't have the IC chip or sitting on the shelf just got older or re-use of old IC is way past its date because it wasn't reset. There is a very good chance just installing a new HP ink cart will clear the problem. I suggest you google for info on your model# printer for all that.
tada -----Willy 