I thought I'd post this in case anyone else has this issue.
I could not get reCaptcha to fully work in my PHPR program. I WOULD get a response from g-recaptcha-response (green check mark on reCaptcha), but my program failed to VERIFY that response with Google.
The problem appeared to be in how the verification process was called:
PHPR uses file_get_contents() to get the verification from Google, and it was that function that was failing - showing different errors.
Sergey pointed me in the direction of my PHP server. After a bit more searching, I set the directive allow_url_fopen = On in my php.ini and now reCaptcha works !!!
Thank you for your quick assistance Sergey!