Coexistence Exchange 2007 and 2013 - Clients on 2013 cant connect to Outlook, OWA works fine

Question

Hi
We are currently running all our users on Exchange 2007. I've installed Exchange 2013 on another hardware following several guides on coexistence between 2007 and 2013.
I'm now testing with a few test users I've migrated from 2007 to 2013.
Everything was working fine until I messed up with something. It's either the certificates and/or Exchange Web Services and/or activating Outlook Anywhere.
Now, all my tests users on Exchange 2013 can connect and send/receive emails on OWA, but Outlook clients cannot connect to Exchange server.
When I start Outlook, I get the error Unable to open the default mail folders
When I try to create a new Outlook profile, I get the error: "The action cannot be completed. The connection to Microsoft Exchange is unavailable. Outlook must be online or connected to complete this action"
When I click on Check Name, I get: "The name cannot be resolved. The connection to Microsoft Exchange is unavailable. Outlook must be online or connected to complete this action" 
Thanks for any help you could provide
Martin

Answer 1

Changed the
ExternalClientAuthenticationMethod  for the 2007 server.
Output for  Get-OutlookAnywhere | fl *method*
ExternalClientAuthenticationMethod : Ntlm
InternalClientAuthenticationMethod : Ntlm
IISAuthenticationMethods           : {Basic, Ntlm, Negotiate}
ExternalClientAuthenticationMethod : Ntlm
InternalClientAuthenticationMethod : Ntlm
IISAuthenticationMethods           : {Basic, Ntlm, Negotiate}
Now everytime I try to create an Outlook profile whose mailbox is on Exchange 2013 it's
asking for credentials.
If I dig further and try to manually configure server settings:
If I specify the Exchange 2013 server and try a 'Check
Name', it says: "Outlook cannot log on. Verify you are connected to the network and are using the proper server and mailbox name. The connection to Microsoft Exchange is unavailable. Outlook must be online or connected to complete this action."
If I specify the Exchange 2007 server and try a 'Check
Name', the server changes for the fqdn of the 2013 server and it does resolve 'Check Name' process. Clicking on Next at this point completes the 'Add new e-mail account wizard". But is I try to start Outlook, I got an error saying "Microsoft Exchange is unavailable"
Any other thoughts on this issue?
Thanks,
Martin