ainge
Hi
Did you tested the spam/junk folder of email. Also need to test the email is working or not on server
Open Joomla global configuration and send a test email. If there is no email received, the problem is from your server its not sending email.
Also check the contact page with default Joomla template and see if it work on that.
Submit a temp super user login for staff via EDIT FIELDS option in first post :http://prntscr.com/mtc08y
I will look on the cause of issue.
Regards