I recently sold my phone which had no problems connecting to wifi when it was available (at home) and using 3G when there was no wifi available.
With my new phone which is a nokia lumia 710 I notice that even using it at home it still has the 3G symbol showing. i have a horrible feeling that its eating up my data even at home.
I've checked within settings and it says its connected to the wifi but also 3G is enabled.
As I've never used this phone before I don't know whether showing the 3G symbol at the top of the screen means its using 3G or whether its using wifi still and it just means 3g is available??
From the Nokia website
Using a Wi-Fi connection is generally faster and less expensive than using a mobile data connection. If both Wi-Fi and mobile data connections are available, your phone uses the Wi-Fi connection.
On my iphone I only ever have either the 3G or the wifi showing - if I connect to wifi this removes the 3G symbol. Have you set up your new phone to connect to your wifi account and router?