outbound email settings failure to send test message
Perhaps your internal mail server uses a different port for smtp? You can see that it's trying to connect to port 25, you might have it configured at a different port?

Alternatively, if you have some kind of command line interface to the machine running the civicrm code, you could try a direct connection using, for example, telnet (details here https://www.port25.com/how-to-check-an-smtp-connection-with-a-manual-telnet-session-2/). 

And finally, you might also look at the dns on the civicrm code machine to make sure your domain for the smtp server is resolving like you expect, and/or trying putting in the ip of the mail server instead of its name.