Now I come to think of this issue, it may not be a problem of 4.5 framework.
I have changed the index from number to string as below, then it works properly.
Thanks for the reading.

if (conn == null) // index is 1 because 0 = localdb        
        connectionString = ConfigurationManager.ConnectionStrings[1].ConnectionString;
        =>         
        connectionString = ConfigurationManager.ConnectionStrings["Action"].ConnectionString;