Hi Sherlyn, We can open each and every identities and check which one is the correct one. Quit Outlook. Hold down Option
key on your Keyboard and open Outlook. The Outlook Database Utility will open. You can see all your Identities in there. Select 1st identity, and make it default (by clicking the settings icon and select Set as Default). See picture below;
Then quit and restart Outlook. If it doesn't open your emails, then try again and this time select the second identity and make it default. Then restart Outlook. Repeat the steps until you find the correct identity.
About restoring from Time Machine : Yes, you CAN "bounce back and forth in time capsule to the date of 4/6/13 which is showing as a "back-up" get my mail and then bring it forward and bounce back to a "back-up" date of today" In other words, you can easily do selective restore from Time Machine without doing a full restore.
Open Time Machine application, choose Enter Time Machine
from the Time Machine menu and the restore interface appears. You can use the timeline on the right side of the window to reach a certain point back in time.
Goto the date 4/6/13. Then in Time Machine, goto your Documents folder, open Microsoft Office folder and restore the correct Identity. Then select it in Outlook using Database Utility.
If you have any trouble following the above steps, please let me know and I'll walk you through it.