I think it doesn't work if you use the same from an to domain if one of the two aren't valid, but should work in general. Make sure both the from and to domains are set to a valid email address registered with the domain email provider and they should go through.
The settings include the "Reply to address", which can be set separately from the from address. The additional parameters aren't necessary for you since it works in some cases, that isn't the problem in your case.
If you need to send authenticated email with username and password, then you have to change to PEAR mail.
Did this help? Tips are appreciated...
