Hey Raj,
I had a similar issue, even my test mail was failing and it was giving similar sort of error.
While setting the db mail, in the SMTP server, I used the loopback address 127.0.0.1./ it can be even your IP address.(Anonymous authentication)
Even my test mail was failing, then I went to IIS Manager, select the Default SMTP server, and under General tab set the IP address as ALL Assigned.
Try this and see if it works.
Cheers,
Pavan.