Mail is getting stuck in Queue (MS Exchange 2013)

SMTP 441 is a failed connection, see here for further reference. Winsock 10061 is Connection Refused. I would say you need to investigate layer 3 and see if you can actually connect to the correct endpoints on the outside world. You can use a site like mxtoolbox to pull up an MX record for a given domain (your intended recipient) and ensure you can name resolve and route to the address. You could also telnet to port 25 and test SMTP.

Next up, look at your Connectors in Exchange. You might have some specific connectors that connect to other internal organizations (parent company or similar), and then an external connector for 'everything else'. It is possible you have a misconfiguration there. In Exchange PowerShell, run Get-SendConnector to get some properties. That might clue you in on the issue.

This was a ISP issue. Solved by logging a call with the ISP.