I want to use the Windows Live Id Authenticaiton in my Asp.Net/MVC web application, but I do not want to use the Login screen provided by Microsoft.
I want to have my custom page for login, take username and password from User and then send these credentials to the Windows Live ID, to Authenticate, and I get back the response if the user is authenticated or not.
Is this possible?
You missed the point of single sign-on authentication. Using that, the user does not provide their credentials to your site, but to the SSO provider. That provider gives you a token which lets you act on behalf of the authenticated user.
The user's credentials are never received by your site.
So no, you cannot, nor should you want to, do this.