How do I get my HP 5610 All-in-One Printer back

Try reinstalling the cartridge. Also listen carefully to the cartridge assembly movement. If you hear any grinding type noises your cartridge is reaching the proper home position. This will cause a cartridge error. If there is any grinding noise you may be in for a long task of realigning your cartridge position to its proper spot. Make sure that the position of the assembly is dead center when you reinstall the cartridge. If it is not move it the center as a starting point. Keep at this moving the assembly in either direction until you no longer hear grinding as the assembly attempts to find its home position. Good luck! Be patient. It may also help to completely unplug the printer for 30 seconds between adjustment attempts.