If you configure Microsoft Outlook 2010 after switching from one computer to another computer or re-install Window Operating system after formatting the hard drive then it seems in most of the cases that Outlook Contacts appears fine after clicking on Navigation Pane but whenever you click on To, Cc or Bcc for composing new mails, the Outlook contacts do not appear.

Resolution:

First make sure that your Contact Folder is the part of OAB (Outlook Address Book). If it is, then you have to move on next step that is reset Outlook Address Book settings.
Configure a Contact Folder as a part of OAB

Steps:
  • Open Microsoft Outlook.
  • Press “CTRL + 3” (combined) and then press “CTRL + 6” (combined).
  • Click right on “Contact Folder” and select Properties from the drag down list.
  • A new Window will appear, go to “Outlook Address Book” Tab and make sure that “Show this folder as an e-mail Address Book” option must be checked.
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If the option already checked or grayed out, then move on further additional steps:

Reset Outlook Address Book Settings:

Steps:
  • Click on “File” tab. Go to “Account Settings”.
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  • A new window will open, click on “Address Books” tab.
  • Under the “Address Books” tab, if the “Outlook Address Book” appears, then close the “Account Settings” dialog box. 
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  • Press “CTRL + SHIFT + B” (combine) to open Address Book dialog box and Go to “Tools” >> Click on “Options”.
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  • An Addressing pop-up box will appear, by default it sets to “Choose automatically” but if you are encounter with error then you can set it to “Contacts”.
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  • Click on “OK” Button.
In case:

If in “Account Settings” >> under the “Address Books” Tab >> Outlook Address Book does not appear, then you have to add it manually by following some steps:
  • Click on “New” under the “Address Books” tab.
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  • Select “Additional Address Books” and click “Next”.
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  • Under “Additional Address Book Types” >> Choose “Outlook Address Book” and click “Next”.
  • Close “Account Setting” dialog box.
  • Shut down Microsoft Outlook and Restart it after few minutes.
Remove Outlook Address Book:

In Microsoft Outlook 2007, 2010 and 2013, you cannot remove “Outlook Address Book”. You have to remove your Outlook account and re-create it.

To do so:Click on "File" tab >> "Account Settings" >> "Account Settings" >> Select Outlook Email account and click on “Remove”.
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It is better to create a new Outlook profile because in most of the cases missing Outlook Address Book service means the Outlook profile is corrupt. 
In future when you want to switch from one computer to another, then save your time by using Plug-gable Window transfer cable (Window Easy Transfer) to move Outlook profile from one PC to another PC.