Thank you for all your follow-up help. The problem is fixed and it turned out to be a GoDaddy situation. The website is hosted with Godaddy and the email is with Rackspace. This would need to change in any website on godaddy that is using an outside source for email.
In Godaddy's CPanel, under the Email section, you select the MX Entry and change the Local Mail Exchanger setting to Remote Mail Exchanger. This allows GoDaddy to send email on a form through a Remote system.
Just in case anyone else has this issue...