Index: moodle/lang/en_utf8/assignment.php
--- moodle/lang/en_utf8/assignment.php Base (1.33)
+++ moodle/lang/en_utf8/assignment.php Locally Modified (Based On 1.33)
@@ -43,6 +43,7 @@
 $string['duedateno'] = 'No due date';
 $string['early'] = '$a early';
 $string['editmysubmission'] = 'Edit my submission';
+$string['starttheassignment'] = 'Start the assignment';
 $string['emailstudents'] = 'Email alerts to students';
 $string['emailteachermail'] = '$a->username has updated their assignment submission
 for \'$a->assignment\'

Index: moodle/mod/assignment/type/online/assignment.class.php
--- moodle/mod/assignment/type/online/assignment.class.php Base (1.88)
+++ moodle/mod/assignment/type/online/assignment.class.php Locally Modified (Based On 1.88)
@@ -125,8 +125,13 @@
             }
             echo $OUTPUT->box_end();
             if (!$editmode && $editable) {
+                if (!empty($submission)) {
+                    $submitbutton = "editmysubmission";
+                } else {
+                    $submitbutton = "starttheassignment";
+                }
                 echo "<div style='text-align:center'>";
-                echo $OUTPUT->single_button(new moodle_url('view.php', array('id'=>$this->cm->id, 'edit'=>'1')), get_string('editmysubmission', 'assignment'));
+                echo $OUTPUT->single_button(new moodle_url('view.php', array('id'=>$this->cm->id, 'edit'=>'1')), get_string($submitbutton, 'assignment'));
                 echo "</div>";
             }