The status in the Windows Live Admin center says "Active" for my custom domain.

All the DNS settings (TXT and MX) in hostgator are correct which I verified with hostgator based on the Windows Live Admin center custom domain setup instructions.

I can login the outlook.com web interface with *** Email address is removed for privacy ***

I can receive AND send emails from *** Email address is removed for privacy *** using the outlook.com web interface.

Using the Outlook 2010 client, I can receive emails to *** Email address is removed for privacy *** 

BUT I cannot send emails since the other server rejects with the following error message:

"Sending reported error (0x800CCC0F): The connection to the server was interrupted. If this problem continues, contact your service administrator or Internet Service Provider (ISP). The server responded 550 5.7.3 Requested action aborted; user not authenticated'

I tried the SMTP setting with 

a) 587, TLS, 

b) 25, SSL

Both did not work.

Would be great if someone could help here.