Caught this question in the Moodle.org forums and remember my frustration the first time I encountered it [link]. The issue is caused sometimes by missing tags (e.g. </tr>, </table>, etc) in HTML or embeddable content which is mis-formatted and then pasted into a summary, label or topic area. The missing tags can be the cause of missing editing icons (even if editing is turned on!). Here’s a screen shot from the specific forum post in question:
As you can see, even though editing appears to be “on”, there’s no option to edit the front page summary area. No worries though, if you encounter this in a course, on your front page or elsewhere it’s possible to still edit the area (so that you can fix the code) without having access to the button/icon. All you need to realize is that many of the editing options for Moodle (in 1.9 at least) are accessible directly by the URL. In this case, to edit the “Front page summary” you just need the URL which you can grab from another site or by remembering this: http://www.yourmoodle.com/course/editsection.php?id=2. If you’re logged in and have the appropriate role, that link will allow you to manually open the editing screen of the summary area without clicking on the icon.
Likewise, for individual courses with this issue in the main summary or one of the topic/weekly summaries the link would be something like this: http://www.yourmoodle.com/course/editsection.php?id=237. It might take some detective work to find the right combination, but this is a quick way to alleviate the stress caused by not being able to edit.
Mary Cooch (@Moodlefairy) has a great video that highlights this very issue and is well worth the watch for ANY Moodle administrator which shows, perhaps, a better tool (by viewing the page source) for finding out what the specific ID is of the summary or label that’s been corrupted. Video on Youtube [http://www.youtube.com/watch?v=DXIhDt5rCmc]