Errormessage Could Not Be Sent. Mailer Error: Smtp Connect() Failed

Moved 2 of our sites to a new server. One of the sites is able to send messages fine, but the other one will not work and instead gives me the following error.

ErrorMessage could not be sent.
Mailer Error: SMTP connect() failed.

On both the old and the new I use SMTP on the one site that works so I set the other one up the same way. I had my host check the ports for me and they are open. I am able to send from my email client and from webmail on the site, but CS-Cart will not work.

I've tried to use PHP Mailer and was unable to get that to work either. They said that I should be able to send using PHP Mailer but I gave up on that and figured I would just try to get the SMTP to work since it's always worked before and it still works on the one site.

Any ideas on where I can check?

Although we had all of the mail settings exactly like the CS-Cart install we have on the same domain name, same server, for whatever reason we had to change "mail. ourwebsite .com" to just "ourwebsite .com". This was basically a new install, of a site we already had installed but moved inside a folder on that domain name. When we used the same mail settings it would not work