I see alot of these issues come into the repair shop I work for.
There are small electronic strips on both the cartridges and the carriage they set into. If you have tried new cartridges, then it could be the contacts on the strip in the back of the carriage.
Try cleaning the contacts with a Q Tip and some alcohol. See if this helps. If not, then most likely the carriage needs replaced.
The issue there is that generally.... There are no parts available for most inkjet printers. Companies like HP, Canon, and Lexmark dont usually have much in the way of parts available. Even the nice inkjet printers are more or less designed to be disposable.
Hope this helps!