This is a more common occurrence than you might expect. The "door" referred to in the error message is actually the portion of your machine that must be lifted up in order to gain access to the ink cartridges for replacing them. You will notice that a protrusion on the lower side of the "door" surface fits into an opening in the surface below the door when the door closes, and this contacts with the door status switch to close the contacts on the switch, telling the machine that the "door" is closed. If indeed the door is fully closed, with nothing obstructing the switch from performing, then that would indicate that either the switch is defective or has come loose. After replacing cartridges, the "door" must be fully closed or you will see the error message. For troubleshooting procedures to solve this problem, go to this link:
http://support.hp.com/us-en/document/c00829896
A test print page may show distorted characters at the beginning, but the characters should be shown correctly towards the end of the test page. If this is not the case then I would suspect that at least one of your cartridges is not seated properly. Open the cartridge access "door," and check the cartridge positions. When you remove and replace a cartridge, the new cartridge should be pushed back as far as it will go and then the front end of the cartridge lifted until you hear it snap into place. When seated properly, the top of the cartridge will be level.