To install Wireless driver for HP Pavilion G4, I followed the instructions here. Basically, I just connected it to the internet using a cable and here is what I did in the terminal (System Tools>Terminal):
su #enter password when prompted sudo yum localinstall --nogpgcheck http://download1.rpmfusion.org/nonfree/fedora/rpmfusion-nonfree-release-stable.noarch.rpm http://download1.rpmfusion.org/free/fedora/rpmfusion-free-release-stable.noarch.rpm yum install akmod-wl akmods --akmod wl modprobe wl
Then, I disconnected the cable and reboot and the Wifi started working. Hope this helps.
Hope this helps.