I'm sorry, for step #1, I just wanted to confirm that you have rebooted all devices.
For step #2, do you mean you have gone to the option "Wireless Setup Wizard" on the printer device, and it's connected to your wireless network name successfully?
- Is there a reset / network reset / default option on printer?
For step #3, when you click on the + button in Print & Fax or Scan, it does not see your hp printer?
- Reinstalling the printer on the computer likely won't help since the iPad does not see the printer either. And even if the driver is corrupted or not installed, the computer should still see the worked printer. But it does not hurt reinstalling the printer software cd disk or download.
For step #4, were you able to reset network settings on the iPad?
All the devices are connected to the same exact wireless network name right?