E-mails not working at all!!

None of the order confirmation e-mails reach the customer.
The test message is failing to reach the receiver too.
I had WP Mail SMTP installed before and it was only failing with the hotmail.com users. For the rest of the customers, including test e-mail, was working. I’ve installed your plugin thinking that will solve the issue with hotmail. However, it is not working with any!
Any idea why? I am using the webmail of our host (on Arvixe), which in our case is mail.flexxslate.com