I just did a fresh install of Zencart and the plugin. I made and update to one file that was causing an issue for me on the installation. The file you mentioned is the file that causes another file to load. By removing the file prevents code in the installation from running.
Try replacing /admin/includes/functions/extra_functions/recaptcha_functions.php with the content in my update:
https://bitbucket.org/pickupman/zenc..._functions.php
OR download the whole plugin at:
https://bitbucket.org/pickupman/zenc...tcha/downloads
What error is showing in your logs/ folder for today?
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