F3.Show(Me, vbModal)

A modal form stops execution in the current form, like an InputBox.

Another point, your logic here is incorrect:

        Do
            lblAttempt.Text = "Enter password. This is attempt number " & Attempt
            Attempt = Attempt + 1
        Loop Until (Attempt = 4) Or (txtPass.Text = Password)

What you're saying is, set the label, increment a variable, then keep looping until you've incremented the variable to 4 (note that the label is set before the incrementation, so it will display "3").  The condition (txtPass.Text = Password) is irrelevant, as txtPass is never updated (the user is never given the chance).

What you should do is have some code like you did before, with the InputBox.  Instead of using an InputBox however, use a modal form.