Código:

Public Class frmSorteos

    Private Sub btnEmpezar_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles btnEmpezar.Click
       

        WebBrowser1.Document.GetElementById("your-name").InnerText = (txtNombre.Text)
        WebBrowser1.Document.GetElementById("TuDNIobligatorio").InnerText = (txtDNI.Text)
        WebBrowser1.Document.GetElementById("your-email").InnerText = (txtEmail.Text)
        WebBrowser1.Document.GetElementById("Tfono").InnerText = (txtTLF.Text)

        WebBrowser1.Navigate("http://www.eldia.es/promociones/?p=904")
        WebBrowser1.Document.GetElementById("submit").InvokeMember("click")



    End Sub


    Private Sub frmSorteos_Load(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles MyBase.Load
        WebBrowser1.Navigate("http://www.eldia.es/promociones/?p=904")
    End Sub
End Class

WebBrowser1.Document.Forms("wpcf7-form").submit()