Hi,
You need to know what is the password with your new WiFi otherwise it won't work (can't hook up). Please try the following setup:
http://www.kremkow.com/1/post/2012/12/wifi-configuration-of-a-hp-deskjet-f4580.html
or use the following guides to set it up as a new printer:
http://h10025.www1.hp.com/ewfrf/wc/manualCategory?cc=us&dlc=en&lc=en&product=3944758&
Regards.