My Contact form works, but I am using the standard Joomla Contact Form. In the Global Configuration, under Mail I have

Mailer: PHP mail function
Mail from: ValidUser@mydomain.com - change this for you
From Name: Can be anything you like
Sendmail Path: /usr/sbin/sendmail - this is right for everyone
SMTP Auth: No
SMTP User: blank
SMTP Auth: blank
SMTP host: localhost

Actually these were the Joomla defaults except for the email address, & the From Name. One issue I've had, though, is if you're using spam assassin, you might have to white list your own domain.

Update here... No improvements. Have gone so far as install fresh version of Joomla at a different location and built-in contact form is working just fine. (Once I remembered to add myself in as a contact!) Beginning to wonder if it isn't that MOSForms module now... Are there better form modules for Joomla out there that are free or very low cost for license? Getting a lot of interest from some people on having their own site managed by Joomla, so I need to know what kind of cost (outside of my own) I'm going to have to make them pay.