Symptoms
Appit icons missing from SharePoint list ribbon
Diagnoses
At one point the settings for the list were changed.
Resolution
1) Click the Gear in the top right of the SharePoint page and select "Edit Page"
2) Select the "Web Part" tab.
3) Select "Web Part Properties"
4) In the menu on the far right there is a drop down for "Toolbar Type" select Full Toolbar and save.