Since you mention the option for Mail for Windows and Mail for Linux, it sounds like you are using Security Assist 1.
Is your hosting account with GoDaddy a windows based account or Linux?
If it is a windows based hosting account select the Mail For Windows option, if it is a linux based hosting account, select Mail For Linux.
You mention that using UE 4, you can send the email successfully, so my guess is that your hosting account is linux based, the windows hosting accounts with GoDaddy are very problematic with using the php mail() function to send emails.
GoDaddy's relay ser er can be rather slow sometimes, it is shared by all of the domains they host, I have seen email take a day to come through using GoDaddy.
In the second step of the Email password wizard, did you set redirects for if the lookup matches or fails? it's a good idea to set these redirects to go to separate pages, this help in determining if the email was sent to the SMTP server or not.
On the last step, make sure the from address is a valid email for your domain. you may also need to leave the from display name setting blank.
you my need to edit the WA_SecurityAssist/MAIL_PHP.php file, change line 211:
$mailObj = mail($mailTo,$mailSubject,$mailContent,$mailHeader);
$mailObj = mail($mailTo,$mailSubject,$mailContent,$mailHeader,"-f".$mailFrom);
it is also possible that the email is coming through but being trapped as spam, don't forget to double check the spam folder.