Hey Henry! 
If there’s no error message being returned, this generally suggests that some custom code you are using is preventing Checkout from occurring, or that some changes were made to your Checkout button and/or form that caused it to break. Unfortunately they are pretty sensitive to change 
As a first point of call it’d be worth removing any custom code that you’re using to see if this fixes it as well. It’s very common to see custom code conflict w/ Cart and Checkout functionality 
If you’re not using any custom code, the kinds of changes to the checkout form that can break it are unfortunately a little tricky to isolate. So I often find that it’s easier to delete your existing Checkout form element and then replace it with a new one to see if this solves the issue.
Otherwise, you can create a test project, enable Ecommerce and compare the default Checkout form to your own. That way you can try and isolate the precise thing that you may have changed accidentally.
Checking both of these things has fixed it for me 99.9% of the time that i’ve run into this issue in the past 