I have tested this with Twenty16 and the issue remains. This indicates an actual issue with WooCommerce itself.
I thought this was because the shipping had been set, however when I tried to set this the loading spinner again was endless.
At this stage you absolutly must contact WooCommerce support https://support.woothemes.com/hc/en-us.
Please inform them:
1) Issue persists with plugins deactivated.
2) With Twenty15/16 active
3) With an increased memory limit added to the wp-config.php file.
4) No console log JS error or 500 server errors.
The above should help expedite the request. In the meantime, I’ll continue to help look for a solution also.
Thanks,
David.