cleaning out the deskjet is easy, first thing you want to do is get a towel with ammonia free windex style shit, or even water. Clean off the clear ribbon that goes from one side of the printer to the other thats behing the cartridge carrier. That calibrates the cartridge and tells it where its at along the page, if its just a little dusty, it can throw printing WAY off. Second, lift the lid to the printer so the cartridges came out to the midway point, then unplug the power so they stay in the middle, proceed to clean out the far right ( where the cartridges hide ) bay with the same towel, and then finish by cleaning off the bottom of the cartridges.
Has this been an on going problem or did it just start with a new set of cartridges?
After you finish, you'll want to recalibrate the printer via the control panel.