Good evening Catherine and welcome to the Events Calendar Support forum!
Thank you for reaching out to us.
We are sorry to hear about the ticket emails not making it through.
I would love to help you with this topic.
To your point, on several installs, it is necessary to add some kind of SMPT plugin for the tickets to be received. What was not clear to me though is if that did solve the issue on your install.
If it did not, then the next step to investigate would be the settings at the very bottom of the following page Events -> Settings -> Tickets.
Basically, the tickets are only sent once a very specific WooCommerce order status is met.
If that still does not work.
Could you please send me a copy of the latest version of your WordPress theme / child theme via a link to a .zip file link (stored Dropbox or Google Drive) so that I can run some tests on my end ? I recommend a private reply for that purpose.
Please ensure you are using the latest files as found on your actual website.
This way I will get access to any updates or customizations you might have made.
Hang in there!
Geoff B.