That error information from the Event Log should be helpful in tracking down the issue.
Some questions:
1) When you installed, did you select to use a security certificate for the Session Central Service and the Session Service? It seems from the message that the binding of the certificate to these services may not be correct. This could be caused by a certificate problem. To get around this issue, don't select a security certificate for these two services. It's not required (though it does provide better security). If you're on a single-box installation, then it's really not needed. See if that gets you around the problem.
2) The other thing I see in the error message that you posted in the "localhost" reference. What's the URL that you're using to access the web service? Are you using "localhost" instead of the machine name? If so, then that won't work, because the security certificate needs to authenticate the actual machine name.
Along that same line, in your screen shot way at the beginning of this thread, we can't see the top of the browser window. That makes it impossible to see if you're having any security certificate errors when you access the GP Web Client site. If you're having any security certificate issues reported, that you will not succeed in connecting to the GP Web Client. You must get any security certificate issues resolved to have success with this.
To summarize, use the security certificate for only the runtime service. Don't use "localhost" in your URL. Use the fully-qualified machine name. Watch for any security certificate errors when you connect to the web client site. if you see any, those errors must be resolved before you will be able to log in.