Try to enable the javascript, if it help to authenticate with the server.
I'm using a linux O.S and my mozilla browser is blocking some pop-up ads and disabling javascript by default.
it is not working if the web server can't communicate with the browser basically its an IP addy to IP addy communication.
P.S When I let the javascript run for a specific website I can communicate with the web server, lets put the main issue that way now.
I'll check if midori has noscript enabled.
I have Mozilla on my laptop with noScript enabled by default I think but it's not too powerful there (if I can still use recaptcha).
The problem is that google recaptcha logs all of the queries from each ip address that uses the recaptcha.
I don't think the problem is with the browser you are using. The issue is with tor. Sometimes you need to use a different exit relay because the current one that you are using has already been flagged by google as a proxy.
I get the same issue sometimes and changing to tor circuit relay fixes this problem.
Tried changing exit nodes, disabling noscript before to weak settings... It won't work still (Linux is more important though for me to focus on).