Hi,
How about repair Outlook profile or re-configure a profile for testing?
If you have something wrong with you Outlook which always pop-up to login, please try to re-configure your Outlook profile or open Control Panel\User Accounts\Credential Manager in problematic computer, then clear the remains credential and try again.
If this issue persists, please run Get-MailboxDatabase | FL Identity,*RPC* to check the value for RpcClientAccessServer.
Besides, please refer to below belog to confirm the steps for migrating Exchange 2007 to Exchange 2013:
http://blogs.technet.com/b/meamcs/archive/2013/07/25/part-2-step-by-step-exchange-2007-to-2013-migration.aspx
Thanks