I had that problem before with 7.2 and now with 7.3 again.
I open SMTP Mailer Module. Now I enter my login data and credentials and make a test with the SMTP Mailer tester at the bottom of the site. And now the strange part:
If I check "Enable SMTP mailer" on top of the page, I get an error "Mail not sent". If I uncheck "Enable SMTP Mailer", I get "Mail successfully sent". The funny part is, even if I change my login or smtp server and enter something wrong, and save this, I also get "Email successfully sent" (if SMTP mailer is not enabled). But if I look at my inbox, email has not been sent, sure not, wrong credentials.
If I send that test email with the correct SMTP credentials, the email goes inbox.
The problem now is, that I need the SMTP Mailer Module. But without checking "Enable", its not enabled. And if I check "Enable", its not working. I made a test registration with enabled SMTP mailer and get: "Joining process has been completed. E-mail has NOT been sent. Unfortunately we could not send the confirmation e-mail. Please, try again later. We appologize for any inconvenience."
I am using your recommended TMDHosting with Dolphin Hosting Plan. They say, its not a server / hosting problem.
Any help would be great.