Gmail doesn't work - "Connection to the server failed"

Hello All,

My iPhone 5 was just replaced because the camera didn't work. When I got the new phone, I did "Restore from backup". This restored all the settings, the music, the notes, and so on. It even has my two email accounts: One Gmail and one IMAP from my university.

The IMAP/university email works fine, although I had to type in my IMAP password the first time I opened the inbox.

The Gmail account does not work. I had to type in my password the first time I opened the inbox, but then it said "Cannot get mail - Connection to server failed".

I deleted the Gmail account and then did "Add new account" in Settings, and when I typed in the password, it displayed check marks next to everything including the password.

Still the same problem. "Connection to the server failed".

The "Add new account" step finishes fine. The error comes when I try to actually open the inbox.

I also cannot send mail from Gmail.

The Gmail App works fine, as does Gmail via Safari, but the Apple Mail App on my iPhone does not work with Gmail.

Any ideas?