We found our problem. A system update changed the sendmail configuration on our server. We run a mail server on the Wordpress server and the PHP.ini was configured to send via sendmail on localhost via port 25 apparently. Our mail server had special configuration to a symbolic link to the sendmail replacement within the mail server's bin. Something like an update and a reboot changed the sendmail back to default replacing out symbolic link hence breaking PHP Mail. We found that using a WP MAIL Plugin as a workaround allowed mail to work but that required configuration of each Wordpress site on the server. We contacted the email server software vendor who tracked down the missing symbolic link issue, and we know have it fixed for the whole server.
The work-around plugin that would make it work individually we used is called WP SMTP http://wordpress.org/extend/plugins/wp-smtp/
(The recommended plugin was WP Mail SMTP http://wordpress.org/extend/plugins/wp-mail-smtp/ but had not been updated in about 2 years so we went with the other one instead)
Not sure if this helps anyone else here, but good luck all!