WiFi showing as connected though no internet

Hello, I tried to help my mum with her new broadband yesterday. She can connect via LAN with the Ethernet cable but cannot connect through WiFi, even though the computer is showing as connected to an unidentified wireless network, which is her wireless network, but can't access the internet. The ISP had me put the DNS settings in, and as it connects wirelessly through my iPhone, are not willing to help. When running the broadband set up CD again, it fails every time in the final check when it comes to internet access. This leads me to believe it's something on the computer stopping this connection. It's not the Firewall as I've tried turning it off and trying. I've reset the Network Adapter as that works on mine occasionally. Does anybody have any advice on what it could be. Many thanks in advance.