Unfortunately, I've only ever used or 'looked at' two of those mods, so I can't really comment, but I would doubt it. The entire email portion of Zen Cart is 3 files. (Discounting language files etc). Functions_email, class.phpmailer and class.smtp. I don't think any of those mods have reason to modify them.

Your problem is also much more fundamental than that. In order to be able to send email, your website has to have access to an email 'transport'.
If you have set the mail transport to SMTP, then there has to be an SMTP server to respond. If you are using sendmail there has to be a senmail binary or wrapper that you can access on the server. Ditto Qmail, and ditto PHP, which is the pHP mail() function, which uses whatever is it configured to use by your host.

Those are provided by your hosting companies servers, and are not working, and no amount of uninstalling or reinstalling or changing settings is going to change that.
Similarly, the fact that one site works and the other not, does not imply that it is an error on your part. Unless they are on the same server in the same folder structure, it has no relevance, other than to show that it can work properly, if the server is working correctly.

The only settings changes you should make are to ensure that you are using something that is recommended by your hosting company. If that fails with a 'Could not instantiate mail function' then they have to fix it.

SMTP on ports other than 25 is an exception to the above, insofar as they require encryption or special behaviour or handshakes/protocols not supported by phpMailer, but that is hopefully not the case here.

'Could not instantiate mail function' is about the same as no dial tone on a phone. You're not going to get anywhere till the service comes back.