Unable to receive or delete emails?

Initially changed my security preferences to below have been Unable to receive or delete emails even from Trash:

I also cannot shutdown computer so have to manually shutdown.

General -

require password to wake up this computer ...

Disable automatic login

Log out after 30 minutes ...

FileVault -

set up a master password

FileVault protection is Off for this account since I don't have enough capacity to set up

Unlocked below but still no difference:

Require password ...

Log out after ..

Have been Advised to either back up/make copy of my messages and reinstall Mail application or take to a Mac store Genius