Intellij doesn't show run button
Right click on src directory and select option Mark Directory As > Sources Root.
In my case Run/Debug buttons disappeared for all projects after updating from IDEA 2019.2 to 2019.3. Tried checking Sources Root, Invalidate Caches, Run/Debug configurations etc - no luck. Only restoring Run/Debug action group helped:
Right click on main toolbar (where the button disappeared) > Customize Menus and Toolbars... > select Run/Debug > Restore Run/Debug.