Inside RequestCaptcha() method you are actually disposing the image which is still being used by picture box.
recaptchaBox.Image.Dispose();
above line is not valid. alternatively you could set
pictureBox1.Image = null;
or if you intend really to dispose the image you can do the following
Image image = recaptchaBox.Image;
recaptchaBox.Image = null;
image.Dispose();
that should solve your problem :)