I found the problem.  Somehow between my first installation of DNN, the uninstallation and re-installation, the hosted environment on GoDaddy changed the SMTP connectivity rules.    The most recent installation requires me to use a relay-smp dns alias which is allowed from my hosted system.

I still can not use any other SMTP server, but it is now clear that it is a firewall/security setting from my provider.

I'm sorry but it is not a relaying problem and neither is a problem of anti-virus/firewall
My web server does not have any antivirus installed and my server mail is configured to allow relaying (I also checked the server mail input log, and nothing comes when SMTP test button is clicked)
How I've reported at the start of this post I've other DNN installation in the same machine with the same settings, and test button work fine for the other installations!
Still I must say it is not a big problem because everything that makes use of emails work fine, only test button don't work!

Hi Sebastian! I've checked more and more times! I've also tried with other settings! I've others twelve installations on the same server and all with the same SMTP settings.