iPhone 4 unable to connect to any Google service on Wi-Fi
It might be related to the DNS on the iPhone.

Go to Settings -> Wi-Fi -> And Connect to your home Wi-Fi Network

Now:


Touch on the "i" icon on the right;
Where it says DNS edit the value for: 8.8.4.4
Go Back to the Wi-Fi networks listing and wait to confirm that the blue tick appears on the left.


This DNS address is from Google, so it will work with everything Google related but also outside of Google universe. 
I've set that address for all my DNS addresses in every machine I use and never had a problem.