Since wihtout entereing credentials you want to authenticate the webapplication request, the only way is
1) You have only the
Request.LogonUserIdentity.Name
to identify the user ,so
2) When you are authenticating the user from windows application , once the authentication is successful then store the corresponding username and
Request.LogonUserIdentity.Name
of the user in a db (Access || xml can also be used)
3) Then once you get a request for the web application ,you will check if
Request.LogonUserIdentity.Name
is available in the above mentioned db.