For a check box to retain its state you need to add a 'checked' directive to the html when you write the form.
echo "<input type='checkbox' name='check1' value='1' ".(($_POST['check1']==1)?"checked":"").">";
For a select box to retain state you need to add a "selected" directive to the option that was selected.
echo "<select name='select1'>";
echo "<option value='1' ".(($_POST['select1']==1)?"selected":"").">";
echo "</select>";
This assumes that your form is being POSTed.