Hi,
If you've deleted the Exchange 2007 public folder database and you get this issue, it may be because the Exchange 2013 databases are referencing the deleted Exchange 2007 public folder database. I've written a blog post which has a walkthrough with screenshots
on how to identify this issue and resolve it. See here:
http://markgossa.blogspot.com/2015/09/exchange-2013-migration-microsoft.html. More helpful information here: https://social.technet.microsoft.com/Forums/office/en-US/88e41b41-b091-4f06-88b3-25d01111ba23/exchange-2007-decom-after-exchange-2013-installation?forum=exchangesvrdeploy
As for the URLs for the virtual directories, make sure that all the names resolve to the IP of one of the Exchange 2013 CAS servers and that the name is on the SSL certificate that the CAS server is using. To get the URLs for the virtual directories, use
the below commands:
Get-EcpVirtualDirectory | fl server,*url*
Get-WebServicesVirtualDirectory | fl server,*url*
Get-UMVirtualDirectory | fl server,*url*
Get-OABVirtualDirectory | fl server,*url*
Get-ClientAccessServer | fl server,AutoDiscoverServiceInternalUri
If the URL is not set (blank) then it defaults to the server FQDN and this then needs to be on the certificate. If you're missing names on the certificate then this can cause password prompts.
Let me know if this answers your question.
Thanks.