Solution:
You have the plugin font-awesome that is overriding iconfont.css definitions and so on, the [class^="icon-"].
It seems that the fontawesome related fonts are not found in the plugin font-awesome.
The plugins/font-awesome/assets/font-awesome.min.css couldn’t find the font ../fonts/fontawesome-webfont.eot
Correct the path or copy the fonts file at this place.
In the browser dev tools, when you unclick fontawesome class, icons are display, it’s just the enqueue priority to modify, it depends if you want to display, font-awesome icons or iconfonts.css icons.