Nothing being logged at all. The email won't be sent! It's never triggered in the first place. There's a setting under WooCommerce emails as to what status gets what email sent - as you said that the new order email is sent when it receives the order - you should check what email gets sent to which orders.
Under WooCommerce - emails, there's an email that'll be sent to the customer when they pay.
It's called "Completed order". Check that it's enabled there.
Then check which status your orders land in after payment. If they don't land in the status that email is tied to, it won't go out.
When that's done and still no luck - let me know, I can see if there's anything else that could be going on.
