I'm having the same problem with a different version of Unity (Unity 5) and different version of the Facebook SDK.
The problem is related to the process created in the method DoesCommandExist() in the file FacebookAndroidUtil.cs. It creates an openssl process to check if it can encrypt an string, but it seems that it gets created without parameters and runs forever, freezing Unity since it calls just after the Start() a WaitForExit().
For the moment, since I'm sure OpenSSL is installed, I'm adding a new line:
if (command.Equals("echo \"xxx\" | openssl base64")) return true;
As soon as the method starts which "solves" the problem of going to facebook API settings.
I've also reported this bug and I'm working on it with someone of the facebook team. Here is the link: https://developers.facebook.com/bugs/984401851605311/
EDIT: We finally found what was causing the problem, the OpenSSL version. It seems that the newer versions of OpenSSL are not compatible with the way the arguments were being passed.
The solution was installing a version of OpenSSL a bit older. Here is the version I installed and works without problems: https://code.google.com/p/openssl-for-windows/downloads/detail?name=openssl-0.9.8k_X64.zip&can=2&q
Thanks to Alans Morales from Facebook Team for suggesting this solution.