Iphone 3g not connecting to wifi

My mom had given me her old Iphone 3g and it connected to our wi-fi in the house and it was under her name. However, it kept on flickering between on and off with the wifi.
As soon as we put the phone in my name, the wi-fi stops working and it won't even search for available networks. I'm wondering how I can get wi-fi available and possibly update to the latest version, it's currently at *iOS 4.2.1