Is the phrase "Ink System Failure" in the message?
First check the cartridges. Remove all of the cartridges. Replace any that are low or empty. Check for damage or a blocked vent. Clear the blockage with a pin. If it is clogged with tape or the orange tab (that was in place during shipping), then remove the tape. Replace any that are damaged. Reinsert the cartridges and make sure that they are fully seated (clicked into place). Check if the error persists when you close the cartridge access door.
Try running the printhead cleaning utility from your computer. (HP Solutions Center under Setting, Print Settings, Printer Toolbox and follow the on-screen directions).
Remove the printhead and clean it. Then reinsert it and make sure it is fully seated. Remove the cartridges, lift the latch handle on the right and lift the print head straight up. This is done with cotton swabs or lint free clothes (coffee filters will work) and distilled or bottled water. During the cleaning do not touch the nozzles; also do not touch the contacts with your fingers. Wet the swab or cloth and wring out the excess water. Wipe the contacts on the printhead with the damp cloth first by wiping up towards the nozzles. Then with another damp cloth wipe the edge between the contacts and the nozzles (work in a right to left motion). Finally wipe down the ramps going away from the nozzles with another cloth. (Wipe each part until there is no ink left.) Dry each area with a fresh cloth.
Next take another damp cloth and wipe the contacts inside the printer. (work from top to bottom.) Dry the area.
Reinstall the printhead and lower the latch handle. Then reinsert the ink cartridges until they snap in. Close the cartridge access cover and check for the error message.
If the error persists, reset the printer. With the printer on, disconnect the power cord from the back of the printer. Disconnect the other end of the cord from the wall outlet. Wait at least 15 seconds and then plug in the cord (first to the wall outlet and then the printer). Turn on the unit.
If the error persists, then either the printhead needs to be replaced or the unit needs service. Unfortunately a new printhead is not returnable if you put it in and find the error persists.
For details and pictures: see http://h10025.www1.hp.com/ewfrf/wc/document?docname=c01458034&tmp_task=solveCategory&lc=en&dlc=en&cc=us&product=3737195#N65
I hope this helps.