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You need to reconnect the printer to the new WiFi network, then only your Mac will recognize it again. Do you have the USB cable came with your printer ?
Cable of any printer will work. They are all same. What you want to do is, just reinstall the printer software again just like you did for the first time. This will register the printer as a new device.
First go to System Preferences > Printer and Fax or Printers and Scanners. Then delete all old entries of printer from there (by clicking the - button)
Then go to this website and download the printer software from here --> http://support.hp.com/us-en/drivers/selfservice/HP-Photosmart-C4700-All-in-One-Printer-series/3794613/model/3794614
Download the software that matches the version of OS X (HP Photosmart Full Feature Software and Drivers). Then go to the Downloads folder and open the downloaded file. Follow the onscreen instructions to install your printer. Choose Wireless setup and use Temporary USB option to setup Wireless while installing. Once you setup Wireless, you can disconnect the USB cable.
Note : If you have the discs came with your printer, you can also use it to reinstall printer.
Please let me know if that didn't work, so I will continue to help you
Hi there, I'm just checking. How is it going ?
On the printer , select the Setup button. Select Wireless > Wireless Setup Wizard. It will find your WiFi network. Select your WiFi network and enter password. Once you are connected to new network, you have to add the printer on your Mac. To do that, go to System Preferences > Printer and Scanners or Print and Fax. Click + button and add your printer.
Let me know how it goes