Cart and contact form not sending mail

About a week ago we noticed that the woocommerce cart was no longer sending out new order notifications. After a few days, we also figured out that the contact form on the site wasn’t working either. When I contacted the hosting company to ask for access to the mail logs, they told me that there was no email server for that particular cloud and the only way email could be sent is via an SMTP plug-in! They had no explanation for why it had been working for over 6 months without one.

I installed an SMTP Plugin and with the help of Microsoft (our email provider), configured it so that test emails from the plugin worked. I also installed a debugger and was getting error emails from that as well (none of which had to do with the cart, contact form or email). However, neither the cart nor the contact form (a Gravity FOrms form) are sending emails still. Any clue what the heck might be going on? I tried installing a different form thinking that adding one post-SMTP installation might work but nope.

Thoughts?

The page I need help with: [log in to see the link]