The phone will connect to the Internet when the mobile data is used from the phone but will not connect when the home wi fi is showing as connected to Bigpond.
The phone will connect to the Internet when the mobile data is used from the phone What kind of phone are we talking about here.....a cellular "smartphone" or a VoIP phone?
Your statement is a little confusing, if you could include a little more detail and a clearer explanation we may be able to help you.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.***William Henley***