Meh, I had this problem too. But its fixed now.
Here are the exact things I did with these plugins that created and fixed the problem, in order.
1.) installed the Simple Contact Form 7
2.) went to edit my form
3.) went to generate the captcha but it said I needed simple captcha
4.) installed the simple captch
5.) went back to edit my form
6.) generated the captcha code
7.) copied the captcha code into my form
8.) saved the form
9.) copied the code into a text widget
10.) refreshed my page and didn't see the image
11.) went back to the generate captcha code
12.) changed the background and foreground color
13.) copy the new generated captcha code
14.) paste new code into form and save the form
15.) think I forgot to save one for the input field tho <!-- I think this caused the problem right here cause... ->
16.) refreshed the page and could see the image now, but the submit did not validate.
17.) decided to start over
18.) deleted the form and made a new one
19.) did everything right this time by changing the color
20.) copied both codes over correctly
21.) saved the form
22.) refresh the page and tested submit, works perfect now.
Thanks for the really simple plugin that does exactly what I need. I might work on extending because I would like the subject to be a drop down box that has only the choice for my categories sections. There is not a live site yet, all testing done with latest version of xampp and wp with only swfflash plugin installed next to it.