No one is doubting that it works for you. But there is a fair number of us who have been posting lately with push problems that can't be explained by the simple answer of having push turned on, or any other settings. To just say that push will work if push is on doesn't solve the issue.
Alright lets level the playing field. Do a forced iPhone backup. Do a factory reset. Activate the phone. DO NOT RESTORE. Create one exchange email account with push notifications. Without going into the mail app, send an email to the phone. If it works, you know it is your data. Restore that data, destroy that email account and reenter it again. If that doesn't fix it then the issue is in the general settings. It is called shotgun troubleshooting, but I can guarantee after you have done all this you will know where the problem lies.