My agents are seeing the CAPTCHA test where you have to put in a number to prove you're not a robot all the time. But when we put in the answer, it never works, even if it's definitely correct.
Your firewall is blocking traffic to Google's reCAPTCHA servers. You should enable outbound traffic on port 80 to Google's servers - see this article for details.
If you are getting the CAPTCHA all the time and can't log in, access your helpdesk from a different IP address. In Admin > Settings under Rate Limiting, you can whitelist your internal IP addresses (so agents connecting from there don't see CAPTCHAs) or disable Rate Limiting altogether (so CAPTCHAs are never shown).