This is a pretty annoying little problem that I’ve seen at least a couple of times over the past several months.
It occurs when you attempt to sync within Outlook, normally following a data transfer or other procedure that involves bringing an existing .PST file into play without jumping through the hoops of importing the data into a new .PST shell.
The solution is actually easy, though it’s not necessarily easy to discover.  All you have to do to solve the problem is select the folder to deliver mail to (Inbox) for each email account.  Under the Account Settings dialog box within Outlook, there is a Change Folder button near the bottom.  This is where the setting is changed.
But what if you can’t even open Outlook?  You can still access the mail settings without running the program.  The easiest way to do this is to click Start > Start Search > type mail and then open the Mail shortcut that appears under the Control Panel heading in the search results.  This opens the standard Outlook mail dialog box as if you were running Outlook.