Question

in some reason if I use this code it sends the form in normal way not with jquery? What could be the problem? thanks

<script>
$(document).ready(function() {
    $("form#formi").submit(function() {
        $(":text, textarea").each(function() {
            if ($(this).val() === "") {
                $('p#error').fadeIn(1000);
                var tyhjia = true;
            }
        });
        if (tyhjia == true) {
            // tyhjia on , joten ei jatketa
        } else {
            // we want to store the values from the form input box, then send via ajax below
            var fname = $('#name').attr('value');
            var lname = $('#email').attr('value');
            $.ajax({
                type: "POST",
                url: "laheta-viesti",
                data: "name=" + fname + "& email=" + lname,
                success: function() {
                    $('form#formi').hide();
                    $('p#valmista').fadeIn(1000);
                }
            });
        }
        return false;
    });
});
</script>

Answer 1

Errors in your javascript are the common cause for this behavior. For example you have defined the tyhjia variable inside the anonymous callback and try to use it outside. I have tried to clean your code a little:

<script type="text/javascript">
    $(document).ready(function() {
        $('form#formi').submit(function() {
            var tyhjia = false;
            $(':text, textarea').each(function() {
                if($(this).val() === '') {
                    $('p#error').fadeIn(1000);
                    tyhjia = true;
                }
            });

            if (tyhjia == true) {
                // tyhjia on , joten ei jatketa
            } else {
                // we want to store the values from the form input box, then send via ajax below
                var fname = $('#name').val();
                var lname = $('#email').val();
                $.ajax({
                    type: 'POST',
                    url: 'laheta-viesti',
                    data: { name: fname, email: lname },
                    success: function() {
                        $('form#formi').hide();
                        $('p#valmista').fadeIn(1000);
                    }
                });
            }
            return false;
        });
    });
</script>

Of course there could be some other errors left. Use FireBug or Chrome Developer Tool and inspect the console for any possible errors reported.

And by the way for doing validation, which is what apparently you are trying to do here, I would very strongly recommend you the jquery validate plugin.