Have you made any changes to the Theme?
I tried viewing your site in Chrome (browser) and the icon fonts are appearing fine.
Do the font's on my demo site appear for you (in Firefox)?
What about the icons on the Font Awesome website. Do they appear for you?
Are you using a CDN (Content Delivery Network) by any chance?
Who is the website host you're using? I believe that WPEngine for example uses CDN's which causes problems for FF and IE as they have a 'cross-domain' issue.
If you are using WPEngine, try adding the following into your .htaccess file.
Header set Access-Control-Allow-Origin "*"