I have a problem establishing connection with Server Explorer in Visual Studio 2012 Ultimate with MS SQL server 2012 Express. Everything is on local machine.
You can see screen shot here - http://s16.postimage.org/4gvo7r5id/se_prob_ss1.png
With System.Data.SqlClient and SqlConnection.Open() everything work fine I'm able to connect and execute SQL scripts (with and without Windows Authentication).
What I tried so far:
In the picture, the server name you are connecting to appears wrong. You indicated you installed SQL Express; it has a default instance name of SQLEXPRESS. So the server you are connecting to should be:
MILLENIUM\SQLEXPRESS
instead of just MILLENIUM.