Instead, I got:
The section "Post Types to be used with this Taxonomy" is completely empty. No way to associate with a type, unless done from the type. The "Labels" section is also empty, with no way to add new labels. See uploaded screenshot.
As a precaution I would like to ensure that this isn't being caused by a plugin and as such I would recommend that you temporarily disable all your non-toolset plugins and try again.
Do whatever you need. We're backed up nightly and nobody's touching the site but you until we can get this issue resolved. Install any plugin you need. If you need a database dump, I can help with that. Everything else, you have access to.
I set WP_DEBUG to true while running PHP 5.6 and got the attached screenshot on the Taxonomy admin page. See attachment and let me know if that helps. I'll change to PHP 7.0 shortly and see if I can get an error message on the white screen.
Let me know if the message in the screenshot helps.