G'day Satmet,
I've had the exact same issue after upgrading a Staff's Iphone 3g to 4S with iOS 5.1.1 on both, after doing a backup on the 3g and restoring that backup on the 4S, i noticed the restore did not contain the password for the email account, (backup restoration's do not store passwords) i also recreated a wireless profile (using iphone configuration utility) to make sure the phone had internet regardless of the carrier, after doing that my client was able to view send receive all emails.
There are quite a few different options in regards to what else you can try, for example resetting factory defaults, recreating the account, Restoring from old backup that worked then enter password for email account.
1. Check Email Password has been entered (settings, mail, accounts, default account, password)
2. Check internet connectivity (open safari or any web application)
a. Connect to a wireless access point to ensure there is no problem with the carrier.
3. Reset Factory Settings. (found in general settings tab at the bottom)
4. Re-create Email account including password,
5. Restore from backup (right click phone, restore from backup, select recent working backup)
6. If you have no backups try restoring Iphone to factory defaults using Itunes
7. If you don't have any backups(unlikely due to 5.1.1 being installed) you can attain the backup file from here
8. Hold down Shift when clicking Restore in Itunes, Select iPhone4,1_5.1.1_9B206_Restore.ipsw wait for the backup to be restored.
9. Re-create Email account including password and all other relevant information.
Best of luck!
Luke
IT Technician & Support Officer.