HI JWTubs
I understand you are unable to connect the printer to the new network.
I can help you with this.
Restoring the Factory Default Settings would be the first thing to do.
I would setup the printer as Adhoc then configure it to Infrastructure.
Click on the airport icon on the Mac located in the top right corner.
Click on the hp printer in the list.
It takes a few minutes to connect and you should get a solid blue light on the printer.
Then print out a configuration page to get the new IP address. Printing a Configuration Report.
Type the IP address in the web browser address bar (Safari) to access the embedded web server for the printer. Click on networking tab, wireless and fill out the information. Apply.
Then go back to the airport icon and reconnect back to your network.
Go to the Apple, system preferences, print and scan, click on the + button, highlight the printer, click on the add button.
Test the printer.
If you need more assistance just let me know.