Apache delivering CSS and JS files, but browsers don't render them
The mime types are probably wrong.
Check they're serving the content with Content-type: text/javascript or Content-type: text/css. You can check this using the Network tab of Chrome's Inspector or Firebug.
You'll need mod_mime, and ensure you have these lines in your httpd.conf:
AddType text/css .css
AddType text/javascript .js
That should do it.