Does any other information come up with the error code? Some 0x errors can be resolved by removing the ink cartridges and resetting the printer.
Disconnect the data cable from the printer (and the computer - optional but often helpful). With the unit on, remove the ink cartridges, then wait until the message "Insert Ink Cartridges" is displayed on the LCD panel. Then unplug the power cord from the back of the printer (unplugging the unit from the wall is optional but again can help). Wait at least 60 seconds, then plug in the power cord (first to the wall and then the printer). Turn on the printer (if needed). Reinsert the ink cartridges when you see the message. Close all open doors and print a calibration page if prompted to do so. Finally, reconnect the USB cable and try printing. If the error occurs again, the all-in-one needs service. You need to decide if it is worthwhile for you if the unit is out of warranty. See http://h10025.www1.hp.com/ewfrf/wc/document?docname=c00489814&tmp_task=solveCategory&lc=en&dlc=en&cc=us&product=422001#N60
for the steps if desired.
If the error includes "Ink System Failure" then other items need to be checked. The cartridges themselves may be clogged or damaged, the printhead may need cleaning or replacing, or the printer may need service. See the link above and follow the link to solutions for errors with "Ink system failure". Note: you can't return a new print head if you replace it and the printer still needs service.
I hope this helps.