An alignment will not complete successfully if the ink is not flowing. A new printer may be the solution. Before you do that you might try a few more troubleshooting steps.
You can remove the ink cartridges and the printhead, unplug the power cord directly from the back of the printer while the printer is still turned on and clean the metal contacts in the printer as described in the following link. Click Here A damp coffee filter or other lint free cloth will work fine. Go ahead and clean the metal contacts ( and nothing else ) on the back of the printhead where it meets the contacts in the printer. Be sure not to touch the printhead where the ink comes out. Once everything is dry, replace the printhead and ink cartridges. Did that make a difference?
If you are using a Windows operating system, you can download and run the HP Hardware Diagnostic Utility for Windows.
Did that make a difference?
You might take a look at the guide for Troubleshooting Print Quality Issues and see if there are any steps that you have not yet taken.