This may be a stupid question, and I'm not implying you don't know what you're doing, but have you gone into the notifications in settings to see if it has notifications turned on?
Do you have it set up as a "GMAIL" account or as an "EXCHANGE" account? I have mine set up as "EXCHANGE" accounts because it was recommended and have never had a problem. Very quick push and notifications work fine.
It's the same way. Except you tap Microsoft exchange, the user name is your email. Password is your email password. Leave domain empty. After you click next the server will pop up. The server is address is m.google.com