My solution:
Go to plugins, find the Really Simple Captcha plugin and click on edit. Find the very first line of the code which starts with:
class ReallySimpleCaptcha
Simply rename ReallySimpleCaptcha to anything you want because I think there’s a conflict with the function which follows (has the same name). I just omitted an “l” in the word Really…
Now activate the plugin…problem solved. I tested the plugin numerous times and it now works just fine.
I’m using the same plugin on another site and didn’t have this problem. Perhaps because I’m using a different theme, not sure.
Anyway, that’s it. Good luck.