Check your string is in the right place in web.config:
<configuration>
<connectionStrings>
<add name=.../>
</connectionStrings>
...
[edit]Spurious
<ConfigSections>
removed - I missed the closing tag :-O - OriginalGriff[/edit]
I missed this the first time round: Take the "()" off your Login.aspx.vb:
Dim connection As String = System.Configuration.ConfigurationManager.ConnectionStrings("Database1").ConnectionString()
Dim mycon As New SqlConnection(connection)
Becomes:
Dim connection As String = System.Configuration.ConfigurationManager.ConnectionStrings("Database1").ConnectionString
Dim mycon As New SqlConnection(connection)