Event registration form does not show submit button when a 100% discount coupon is used
That looks like a bug, but I notice your CiviCRM is 4 versions behind the current one, so I'd update your CiviCRM first before doing anything else.

I have seen some similar issues in the past - when you have an on-site payment processor, there is some logic that hides the payment form when no payment is due. Perhaps in combination with an off-site processor like Paypal Standard, the hiding of the payment form turns into hiding the submit button.