I'm currently trying to solve (not bypass, just send the answer) reCAPTCHA via HttpWebRequests but I'm failing at one parameter.

I'm using this site for testing purposes: http://patrickhlauke.github.io/recaptcha/

What I've done so far:
[quote]
[list]
[*]Send GET Request -> http://patrickhlauke.github.io/recaptcha/
[*]Parse -> data-sitekey="[color=#FF0000]6Ld2sf4SAAAAAKSgzs0Q13IZhY02Pyo31S2jgOB5[/color]"
[*]Send GET Request -> https://www.google.com/recaptcha/api2/anchor?k=[color=#FF0000]6Ld2sf4SAAAAAKSgzs0Q13IZhY02Pyo31S2jgOB5[/color]&co=[color=#FF0000]aHR0cHM6Ly9wYXRyaWNraGxhdWtlLmdpdGh1Yi5pbzo0NDM[/color]
[list]
[*]The second red value is a BASE64 String which contains the Domain Name + Port specified for the data-sitekey -> BASE64_ENCODE([color=#FF0000]https://patrickhlauke.github.io:443[/color])
[/list]
[*]Parse -> id="recaptcha-token" value="[color=#FF0000]03AHJ_VutqBTwUTg...[/color]"
[*]Send GET Request -> https://www.google.com/recaptcha/api2/frame?c=[color=#FF0000]03AHJ_VutqBTwUTg...[/color]
[*]Parse -> recaptcha.frame.Main.init("[....]") between [color=#FF0000][\x22rresp\x22,\x22[/color] and [color=#FF0000]\x22[/color] and you will get one more [color=#FF0000]03AHJ_VuuUAmYWcUwr5PT...[/color]
[*]Parse -> between [color=#FF0000][\x22pmeta\x22,[\x22[/color] and [color=#FF0000]\x22[/color] and you will get the "instruction" what kind of pictures you'll have to click, for example [color=#FF0000]/m/07jdr[/color] (this is the name/id/whatever for [color=#FF0000]Select all images with trains.[/color])
[*]Send GET Request (this is the captcha image itself) -> https://www.google.com/recaptcha/api2/payload?c=[color=#FF0000]03AHJ_VuuUAmYWcUwr5PT...[/color]&k=[color=#FF0000]6Ld2sf4SAAAAAKSgzs0Q13IZhY02Pyo31S2jgOB5[/color]
[*](Download or just show the captcha image in your Windows Form)
[*]Send POST Request (Captcha Answer) -> https://www.google.com/recaptcha/api2/userverify?k=[color=#FF0000]6Ld2sf4SAAAAAKSgzs0Q13IZhY02Pyo31S2jgOB5[/color]
[list]
[*]POST Parameters:
[list]
[*]v = r20160502112552 (API Version? It's everytime the same value)
[*]c = [color=#FF0000]03AHJ_VuuUAmYWcUwr5PT...[/color]
[*]response = eyJyZXNwb25zZSI6IjMsNSw4In0. -> BASE64 String which contains the IDs of the images you have clicked (first image has ID 0) -> BASE64_ENCODE([color=#FF0000]{"response":"3,5,8"}[/color])
[*]t = 11228 (don't know, everytime different but same as ct - reCAPTCHA also success without this param)
[*]ct = 11228 (don't know, everytime different but same as t - reCAPTCHA also success without this param)
[*]bg = !r6lHI_LEBsGBAVBBxz2yqSQttAUHAAAAiVcAAAAFDw... [b][color=#32CD32]THIS IS MY PROBLEM[/color][/b]
[/list]
[/list]
[/list]
[/quote]

If everything was correct you will receive a JSON String with again one more [color=#FF0000]03AHJ_...[/color] which you can finally use for the main website you want to enter/login/whatever. Just use it in the POST Request, for example:

[quote]
[list]Send POST Request -> https://mysite.com/login
[list]
[*]POST Parameters:
[list]
[*]username = myusername123
[*]password = mypassword123
[*]g-recaptcha-response = the new [color=#FF0000]03AHJ_...[/color]
[/list]
[/list]
[/list]
[/quote]

But how do I get the "bg" value? This is the only parameter which makes me failing at logging into a website. I tried it with some Chrome Extensions which allow me to block/edit outgoing HttpRequests. So I tried to edit and also remove for example the params "ct" or "t" and "v" and as stated above the captcha also succeeded without these params. Only the 03AHJ_ value (captcha image) and the bg value are important, otherwise reCAPTCHA will send me a new captcha to solve as JSON String.