Thanks for the reply.
I just read those links you sent me and installed the E-mail Archive Manager. My order confirmation e-mails are being archived, but I am not getting a Confirmation E-mail of the order nor is my customer getting an order confirmation. (Yikes!) I used to use a classic hosting plan at GoDaddy. I moved the old cart to a new cPanel plan. (I'm not sure if the e-mail confirmations were working at that point but everything else was working.) Once everything appeared to be working, I did the Zen Cart upgrade to Version 1.5.4. I added on the Alysa Rounded Template and Image Handler 4. (The e-mails were already not working before I installed Image Handler 4, however, so that cannot be the issue.) I really did not make any changes other than to the Alysa Rounded Template (just looking at the old changes of the previous version and re-creating those changes with the new version). Just now I tried changing e-mail delivery from PHP (though it always worked with PHP) to smtpauth, but that did not help.
When I look in the logs you mentioned, I see a "myDEBUG" log, but I'm not sure if it applies to this issue or what it means. It states: "[19-Mar-2015 03:00:44 UTC] PHP Warning: mysqli_connect(): (42000/1226): User 'myusername' has exceeded the 'max_user_connections' resource (current value: 30) in /home/myhostingaccountname/public_html/mywebsitename/catalog/includes/classes/db/mysql/query_factory.php on line 62"
When I created and "ran" the email_debug.php for the Advanced E-mail Debugging suggestion on one of the links you provided, it said the e-mail failed to send, and I got this error message: "SMTP server error: Please turn on SMTP Authentication in your mail client." It gave me some error numbers and then said that my domain name "is not permitted to relay through this server without 550 authentication."
Do I turn on SMTP authentication somewhere in the ZenCart or somewhere in my hosting account? Please help! Thank you! :-)