This question has been answered by paulp. See the first response.
Not entirely sure how this captcha is working but i suspect it just generates an image based on a random math value. If you use dev tools to inspect the image you can see the rand string on the end of the src. Try using this number to get yourself logged in at least.
This doesn't look like a google recaptcha service but in any case google did drop recaptcha v1 a while back I believe, so you'll need to use recaptcha v2.
I dont see how the captcha prevents you from logging into the manager?
I dont see how the captcha prevents you from logging into the manager?
If you enable it via the system setting it adds it to the login screen, hence its not showing so he cant log in.
Try logging into phpmyadmin and searching the system settings table in the database for captcha and see if you can disable it from there ( change the value from 1 to 0 )
I dont have it installed on my sites so can't test it, but make sure you have deleted everything in the core >> cache folder via FTP and then try the manager login screen again